{"id":1024,"date":"2020-08-18T18:35:09","date_gmt":"2020-08-18T22:35:09","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/?post_type=chapter&#038;p=1024"},"modified":"2021-07-12T17:07:21","modified_gmt":"2021-07-12T21:07:21","slug":"deferred-annuities","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/chapter\/deferred-annuities\/","title":{"raw":"5.5 Deferred Annuities","rendered":"5.5 Deferred Annuities"},"content":{"raw":"<div class=\"textbox textbox--learning-objectives\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Learning Outcomes<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nCalculate deferred withdrawals from a retirement fund and deferred payments on a debt.\r\n\r\n<\/div>\r\n<\/div>\r\nTo understand [pb_glossary id=\"2159\"]deferred annuities[\/pb_glossary], let us first go back and examine the definition of an annuity. An [pb_glossary id=\"2160\"]annuity[\/pb_glossary] is \u201ca series of equal-sized payments, at regular intervals, over a fixed period of time.\u201d What then does it mean to defer this annuity?\u00a0 It means to delay (or defer) the regular payments for a period of time.\r\n\r\nBecause there is a deferral period and a payment (annuity) period, there are actually two parts to the problem:\r\n\r\n<a href=\"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-content\/uploads\/sites\/971\/2020\/08\/5-5-Fig1.jpg\"><img class=\"wp-image-2558 size-full aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-content\/uploads\/sites\/971\/2020\/08\/5-5-Fig1.jpg\" alt=\"Timeline of a deferred annuity\" width=\"90%\" \/><\/a>\r\n\r\n<span style=\"color: #000000\"><strong>Part 1<\/strong><\/span>: Deferral Period\r\n<ul>\r\n \t<li>There are no payments in part 1 (PMT<sub>1<\/sub> = 0).<\/li>\r\n \t<li>The only money being added to the initial balance (PV<sub>1<\/sub>) is the interest being earned (or charged).<\/li>\r\n \t<li>The ending balance from the deferral period (FV<sub>1<\/sub>) equals the starting balance for the annuity (PV<sub>2<\/sub>).<\/li>\r\n<\/ul>\r\n<span style=\"color: #000000\"><strong>Part 2<\/strong><\/span>: Annuity with Regular Payments\r\n<ul>\r\n \t<li>Payments are being made or withdrawn (PMT<sub>2<\/sub>).<\/li>\r\n \t<li>Assume the final future value (FV<sub>2<\/sub>) equals 0 unless told otherwise.<\/li>\r\n<\/ul>\r\nSee the sections below for key formulas, tips and examples related to deferred annuities calculations.\r\n<h1>Examples of Deferred Annuities<\/h1>\r\nThe most common example of a deferred annuity is a retirement fund where the investor is not yet ready to retire. They defer their withdrawals (payments) until they retire. In the mean time, the fund earns interest. The fund continues to earn interest as the investor withdraws money from the fund.\r\n\r\nOther possible examples of deferred annuities are student loans[footnote]A student loan is a special case of a deferred annuity in that if the student receives a government-sponsored student loan, they do not need to pay any interest while they are in school.[\/footnote] and in-store credit cards that offer \u201cpay nothing for 18 months\u201d promotions on their in-store credit cards. These are both less than perfect examples of deferred annuities in that they both come with exceptions.\r\n\r\nIn the case of the student loan, the student defers repaying the loan until after they have finished school[footnote]If the Government of Canada has given out the student loan, then it is a special case of a deferred annuity. The student does indeed defer their payments until after they have finished school (they can wait up to 6 months after they are done school to start their payments).[\/footnote]. What is special about this case is that the Government does not charge them any interest during the deferment. If the loan is granted by a bank or other financial institution, then the student gets charged interest during the deferral period.\r\n\r\nIn the case of \u201cpay nothing for 18 months\u201d promotion, the credit card holder defers payments (possibly waits for 18 months to start making payments) on the card. These cards and promotions come with a lot of fine print and exceptions. The credit card example becomes like a deferred annuity if the credit card holder fails to pay off the entire balance on the card before the 18 months is up. They get back-charged interest on the amount borrowed. If, after this happens, they set up a payment schedule to repay the amount owing on the card with regular, equal-sized payments, then the credit card example becomes a deferred annuity example.\r\n<h1>Saving for Retirement EXAMPLES<\/h1>\r\nIf you search the web for \u2018deferred annuity\u2019 \u2014\u00a0the savings deferred annuity related to planning for retirement will come up in at least the top 5 searches. It is the most common type of deferred annuity. When people plan for their retirement, they start saving before they retire. They usually do not need to withdrawn money from a retirement fund until they retire. In other words, they defer the withdrawals until retirement. Let us look at an example of this to better understand this type of deferred annuity.\r\n\r\n&nbsp;\r\n<h2>Example 5.5.1: Deferred Withdrawals from a Retirement Fund with BGN Off<\/h2>\r\nAnn and Sue sell their recreation property. They make $245,000 on the sale and deposit it immediately into a retirement fund. The fund earns 2.45%, compounded monthly, for the entire time.\u00a0\u00a0 Exactly ten years after the sale, Ann retires. They now want to start supplementing their income with payments from the retirement fund. They want the payments to start one month after Ann retires.\u00a0 They want these payments to last for 5 years. How much can they withdraw per month from the retirement fund?\r\n\r\nLet us first organize this information into a time diagram:\r\n\r\n<a href=\"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-content\/uploads\/sites\/971\/2020\/08\/5-5-Fig2.jpg\"><img class=\"wp-image-2567 size-full aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-content\/uploads\/sites\/971\/2020\/08\/5-5-Fig2.jpg\" alt=\"Timeline of deferred annuity in Example 1\" width=\"95%\" \/><\/a>\r\n<ul>\r\n \t<li>The deferral period (part 1) occurs first.<\/li>\r\n \t<li>The deposit of $245,000 occurs at the very beginning of this deferral period.<\/li>\r\n \t<li>No payments nor withdrawals are made for the first 10 years (only interest is added for these 10 years).<\/li>\r\n \t<li>After the 10 years is complete, part 2, the annuity, begins.<\/li>\r\n \t<li>One month after the start of part 2 (annuity), the first withdrawal occurs.<\/li>\r\n \t<li>These withdrawals repeat for 5 years until no money is left in the annuity.<\/li>\r\n<\/ul>\r\nThe tricky part with these types of problems with two parts is determining which part to start with. Start where the \"known\" money is. In this example, we know that Ann and Sue deposit $245,000 immediately (PV<sub>1<\/sub> = 245,000). For this reason, we will start with part 1 because PV<sub>1<\/sub> is known.\r\n\r\n<span style=\"color: #000000\"><strong>Part 1<\/strong><\/span>: Let us now organize the information for Part 1 into a BAII Plus table:\r\n<table class=\"lines aligncenter\" style=\"border-collapse: collapse;width: 90%\" border=\"0\">\r\n<thead>\r\n<tr>\r\n<th class=\"border\" style=\"width: 8%\">B\/E<\/th>\r\n<th class=\"border\" style=\"width: 8%\">P\/Y<\/th>\r\n<th class=\"border\" style=\"width: 8%\">C\/Y<\/th>\r\n<th class=\"border\" style=\"width: 20%\">N<sub>1<\/sub><\/th>\r\n<th class=\"border\" style=\"width: 8%\">I\/Y<\/th>\r\n<th class=\"border\" style=\"width: 12%\">PV<sub>1<\/sub><\/th>\r\n<th class=\"border\" style=\"width: 8%\">PMT<sub>1<\/sub><\/th>\r\n<th class=\"border\" style=\"width: 28%\">FV<sub>1<\/sub><\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td class=\"border\" style=\"width: 8%\">\u2013\u2013<\/td>\r\n<td class=\"border\" style=\"width: 8%\">12<\/td>\r\n<td class=\"border\" style=\"width: 8%\">12<\/td>\r\n<td class=\"border\" style=\"width: 20%\">10\u00d712=120<\/td>\r\n<td class=\"border\" style=\"width: 8%\">2.45<\/td>\r\n<td class=\"border\" style=\"width: 12%\">+245,000<\/td>\r\n<td class=\"border\" style=\"width: 8%\">0<\/td>\r\n<td class=\"border\" style=\"width: 28%\"><strong>CPT<\/strong> <span style=\"color: #ff0000\">-312,939.05<\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<ul>\r\n \t<li>Since there are no payments, B\/E doesn't matter (that is why '[pb_glossary id=\"3272\"]\u2013\u2013[\/pb_glossary]' <strong>\u00a0<\/strong>is set for B\/E).<\/li>\r\n \t<li>Because the interest rate is 2.45% compounding monthly, I\/Y = 2.45 and C\/Y = 12.<\/li>\r\n \t<li>Because there are no payments, match P\/Y to C\/Y (P\/Y = 12).<\/li>\r\n \t<li>The deferral period lasts 10 years, so N<sub>1<\/sub> = 10\u00d712=120.<\/li>\r\n \t<li>Remember, the $245,000 deposit occurs at the very beginning so PV<sub>1 <\/sub>= +245,000.<\/li>\r\n \t<li>There are no payments for the deferral period so PMT<sub>1<\/sub> = 0.<\/li>\r\n \t<li><strong>CPT<\/strong> \u00a0FV<sub>1 <\/sub>= \u2212312,939.05. Ann and Sue's initial deposit grows to $312,939.05 after 10 years due to the interest earned on the deposit.<\/li>\r\n \t<li>The $312,939.05 (FV<sub>1<\/sub>) will become the starting value for the annuity in part 2 (PV<sub>2<\/sub>).<\/li>\r\n<\/ul>\r\n<span style=\"color: #000000\"><strong>Part 2<\/strong><\/span>: Let us now organize the information for Part 2 into a BAII Plus table:\r\n<table class=\"lines aligncenter\" style=\"border-collapse: collapse;width: 90%\" border=\"0\">\r\n<thead>\r\n<tr>\r\n<th class=\"border\" style=\"width: 8%\">B\/E<\/th>\r\n<th class=\"border\" style=\"width: 8%\">P\/Y<\/th>\r\n<th class=\"border\" style=\"width: 8%\">C\/Y<\/th>\r\n<th class=\"border\" style=\"width: 20%\">N<sub>2<\/sub><\/th>\r\n<th class=\"border\" style=\"width: 8%\">I\/Y<\/th>\r\n<th class=\"border\" style=\"width: 12%\">PV<sub>2<\/sub><\/th>\r\n<th class=\"border\" style=\"width: 28%\">PMT<sub>2<\/sub><\/th>\r\n<th class=\"border\" style=\"width: 8%\">FV<sub>2<\/sub><\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td class=\"border\" style=\"width: 8%\">END<\/td>\r\n<td class=\"border\" style=\"width: 8%\">12<\/td>\r\n<td class=\"border\" style=\"width: 8%\">12<\/td>\r\n<td class=\"border\" style=\"width: 20%\">5\u00d712=60<\/td>\r\n<td class=\"border\" style=\"width: 8%\">2.45<\/td>\r\n<td class=\"border\" style=\"width: 12%\">+312,939.05<\/td>\r\n<td class=\"border\" style=\"width: 28%\"><strong>CPT<\/strong> <span style=\"color: #ff0000\">\u22125,546.95<\/span><\/td>\r\n<td class=\"border\" style=\"width: 8%\">0<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<ul>\r\n \t<li>The payments start one month after Ann retires (in one payment interval), so B\/E = [pb_glossary id=\"2089\"]END[\/pb_glossary].<\/li>\r\n \t<li>Because the interest rate is still 2.45% compounding monthly, I\/Y = 2.45 and C\/Y = 12.<\/li>\r\n \t<li>Ann and Sue receive monthly payments so P\/Y = 12.<\/li>\r\n \t<li>They want these payments to last 5 years so, N<sub>2<\/sub> = 5\u00d712=60.<\/li>\r\n \t<li>Use the (positive) value of FV<sub>1<\/sub> for PV<sub>2<\/sub>. So, PV2 = +<span style=\"color: #000000\">312,939.05<\/span>.<\/li>\r\n \t<li>There is no money left at the end of 5 years so FV<sub>2<\/sub> = 0.<\/li>\r\n \t<li>Compute PMT<sub>2<\/sub> to get the size of Ann and Sue's monthly withdrawals.<\/li>\r\n<\/ul>\r\nConclusion: Ann and Sue can withdraw $5,546.95 per month from their retirement fund.\r\n\r\n&nbsp;\r\n<h2>Example 5.5.2: Deferred Withdrawals from a Retirement Fund with BGN On<\/h2>\r\nWhat would change in Example 1 if Ann and Sue made the first withdrawal exactly 10 years after the sale of their property?\u00a0 Ie: what if their first withdrawal occurred the day that Ann retired?\r\n\r\nLet us first look at the timeline for this problem:\r\n\r\n<a href=\"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-content\/uploads\/sites\/971\/2020\/08\/5-5-Fig3.jpg\"><img class=\"wp-image-2571 size-full aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-content\/uploads\/sites\/971\/2020\/08\/5-5-Fig3.jpg\" alt=\"Timeline of deferred annuity for Example 2\" width=\"95%\" \/><\/a>\r\n<ul>\r\n \t<li><span style=\"color: #000000\"><strong>Part 1 <\/strong><\/span>is the same as in Example 1, so we do not need to redo those calculations.<\/li>\r\n \t<li><span style=\"color: #000000\"><strong>Part 2<\/strong><\/span> has changed. The first withdrawal (PMT<sub>2<\/sub>) now occurs exactly at the start (beginning) of that annuity.<\/li>\r\n \t<li>This means we set the calculator to [pb_glossary id=\"2088\"]BGN[\/pb_glossary] when calculating the annuity payments in part 2 (PMT<sub>2<\/sub>):<\/li>\r\n<\/ul>\r\n<table class=\"lines aligncenter\" style=\"border-collapse: collapse;width: 90%\" border=\"0\">\r\n<thead>\r\n<tr>\r\n<th class=\"border\" style=\"width: 8%\">B\/E<\/th>\r\n<th class=\"border\" style=\"width: 8%\">P\/Y<\/th>\r\n<th class=\"border\" style=\"width: 8%\">C\/Y<\/th>\r\n<th class=\"border\" style=\"width: 20%\">N<sub>2<\/sub><\/th>\r\n<th class=\"border\" style=\"width: 8%\">I\/Y<\/th>\r\n<th class=\"border\" style=\"width: 12%\">PV<sub>2<\/sub><\/th>\r\n<th class=\"border\" style=\"width: 28%\">PMT<sub>2<\/sub><\/th>\r\n<th class=\"border\" style=\"width: 8%\">FV<sub>2<\/sub><\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td class=\"border\" style=\"width: 8%\">END<\/td>\r\n<td class=\"border\" style=\"width: 8%\">12<\/td>\r\n<td class=\"border\" style=\"width: 8%\">12<\/td>\r\n<td class=\"border\" style=\"width: 20%\">5\u00d712=60<\/td>\r\n<td class=\"border\" style=\"width: 8%\">2.45<\/td>\r\n<td class=\"border\" style=\"width: 12%\">+312,939.05<\/td>\r\n<td class=\"border\" style=\"width: 28%\"><strong>CPT<\/strong> <span style=\"color: #ff0000\">\u22125,535.64<\/span><\/td>\r\n<td class=\"border\" style=\"width: 8%\">0<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h4>Conclusions:<\/h4>\r\n<ul>\r\n \t<li>The amount withdrawn by Ann and Sue decreases slightly from $5,546.95 to $5,535.64 when they make the first withdrawal on the day that Ann retires.<\/li>\r\n \t<li>Withdrawing the first payment one month earlier means that Ann and Sue will miss out on the interest that would have been earned on that payment.<\/li>\r\n \t<li>This is because the money in the annuity continues to earn interest as the withdrawals are being made.<\/li>\r\n \t<li>As a result, Sue and Ann withdraw $11.31 less per month if they make the first withdrawal exactly 10 years after the sale of their property.<\/li>\r\n<\/ul>\r\n&nbsp;\r\n<h1>Interest Earned when Saving for Retirement<\/h1>\r\nAgain we use same interest formula:\r\n<p style=\"text-align: center\">[latex] \\begin{align*} \\textrm{Interest Earned} &amp;= \\textrm{Money Out} - \\textrm{Money In} = \\textrm{\\$ OUT} - \\textrm{\\$ IN} \\end{align*} [\/latex]<\/p>\r\nWe need to be careful when calculating money in and money out for deferred annuities.\r\n<ul>\r\n \t<li>What money was deposited in the account? Only the initial deposit (PV<sub>1<\/sub>) is considered money in ($ IN).<\/li>\r\n \t<li>What money do we take out (withdraw)? Only the regular withdrawals (PMT<sub>2<\/sub>) and final withdrawal (FV<sub>2<\/sub>) in part 2 are considered to be money out ($ OUT).<\/li>\r\n \t<li>Because FV<sub>1<\/sub> does not get withdrawn but instead becomes the starting balance for the annuity (PV<sub>2<\/sub>), it is not included in our interest calculation. The money is neither being deposited nor withdrawn.<\/li>\r\n<\/ul>\r\n<table class=\"no-lines aligncenter\" style=\"border-collapse: collapse;width: 100%;height: 52px\">\r\n<thead>\r\n<tr style=\"height: 18px\">\r\n<th style=\"width: 12.5%;height: 18px\">PV<sub>1<\/sub><\/th>\r\n<th style=\"width: 12.5%;height: 18px\">Interest<sub>1<\/sub><\/th>\r\n<th style=\"width: 12.5%;height: 18px\">PMT<sub>1<\/sub><\/th>\r\n<th style=\"width: 12.5%;height: 18px\">FV<sub>1<\/sub><\/th>\r\n<th style=\"width: 12.5%;height: 18px\">PV<sub>2<\/sub><\/th>\r\n<th style=\"width: 12.5%;height: 18px\">Interest<sub>2<\/sub><\/th>\r\n<th style=\"width: 12.5%;height: 18px\">PMT<sub>2<\/sub><\/th>\r\n<th style=\"width: 12.5%;height: 18px\">FV<sub>2<\/sub><\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 12.5%;height: 16px\"><strong>Initial Deposit<\/strong><\/td>\r\n<td style=\"width: 12.5%;height: 16px\"><strong>+ % Earned<\/strong><\/td>\r\n<td style=\"width: 12.5%;height: 16px\"><strong><span style=\"color: #000000\">+ $0<\/span><\/strong><\/td>\r\n<td style=\"width: 12.5%;height: 16px\"><span style=\"color: #ff0000\"><strong>=Ending Balance Part 1<\/strong><\/span><\/td>\r\n<td style=\"width: 12.5%;height: 16px\"><strong><span style=\"color: #000000\">=Starting Balance Part 2<\/span><\/strong><\/td>\r\n<td style=\"width: 12.5%;height: 16px\"><strong>+ % Earned<\/strong><\/td>\r\n<td style=\"width: 12.5%;height: 16px\"><span style=\"color: #ff0000\"><strong>=<\/strong> <strong>Regular Withdrawals<\/strong><\/span><\/td>\r\n<td style=\"width: 12.5%;height: 16px\"><strong><span style=\"color: #ff0000\">+ Final<\/span><span style=\"color: #ff0000\"> Wit<\/span><span style=\"color: #ff0000\">hdraw<\/span><span style=\"color: #ff0000\">al<\/span><\/strong><\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px\">\r\n<td style=\"width: 12.5%;height: 18px\">$ IN<\/td>\r\n<td style=\"width: 12.5%;height: 18px\">$ IN<\/td>\r\n<td style=\"width: 12.5%;height: 18px\"><strong>\u2013\u2013<\/strong><\/td>\r\n<td style=\"width: 12.5%;height: 18px\"><strong><span style=\"color: #ff0000\">\u2013\u2013<\/span><\/strong><\/td>\r\n<td style=\"width: 12.5%;height: 18px\"><strong>\u2013\u2013<\/strong><\/td>\r\n<td style=\"width: 12.5%;height: 18px\">$ IN<\/td>\r\n<td style=\"width: 12.5%;height: 18px\"><span style=\"color: #ff0000\">$ OUT<\/span><\/td>\r\n<td style=\"width: 12.5%;height: 18px\"><span style=\"color: #ff0000\">$ OUT<\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nThis gives us the following equation for interest earned:\r\n<p style=\"text-align: center\">[latex] \\begin{align*} \\textrm{Interest Earned} &amp;= \\textrm{\\$ OUT} - \\textrm{\\$ IN}\\\\ &amp;=( \\textrm{Regular Withdrawals}+\\textrm{Final Withdrawal}) - \\textrm{Initial Deposit}\\\\ &amp;= ( \\textrm{PMT}_2\\times\\textrm{N}_2+\\textrm{FV}_2)-\\textrm{PV}_1 \\end{align*} [\/latex]<\/p>\r\n&nbsp;\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Check Your Knowledge 5.5.0<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nCalculate the amount of interest Ann and Sue will earn in on their retirement savings plan from Example 2:\r\n\r\n[h5p id=\"92\"]\r\n\r\n[h5p id=\"93\"]\r\n\r\n<\/div>\r\n<\/div>\r\n&nbsp;\r\n<h1>Deferring Payments on a Debt EXAMPLE &amp; Key Takeaways<\/h1>\r\nIt is quite common to defer payments when purchasing items, especially in retail.\u00a0 A retailer purchases their goods from a supplier.\u00a0 If cash flow is an issue for the retailer, they can often choose to defer the payments on the shipment until a later date.\u00a0 It is also common when consumers purchase items using \u201cin-store\u201d credit cards.\u00a0 Some stores have \u201cPay Nothing\u201d promotions for their customers.\u00a0 If a customer purchases goods from the store on the in-store credit card, they can choose to make no payments on their purchase for a certain amount of time (6 months, 12 months, 18 months,\u2026).\r\n\r\nIn the above cases, the retailer or customer owes the value of the amount of goods they purchased.\u00a0 They make no payments for a certain amount of time (they defer their payments).\u00a0 After the deferral period has passed, they make payments to repay the value of the goods plus the interest charged during the deferral period.\u00a0 See the timeline describing this process:\r\n\r\n<a href=\"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-content\/uploads\/sites\/971\/2020\/08\/5-5-Fig1-1.jpg\"><img class=\"wp-image-2562 size-full aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-content\/uploads\/sites\/971\/2020\/08\/5-5-Fig1-1.jpg\" alt=\"Timeline of a deferred annuity\" width=\"90%\" \/><\/a>\r\n\r\n<strong>Part 1<\/strong>: The initial amount owing gathers interest.\u00a0 There are no payments in part 1 (the deferral period).\u00a0 The only money being added to the balance is the interest being charged.\u00a0 This problem is a compound interest problem (Chapter 4):\r\n\r\n<strong>Part 2<\/strong>: Payments are now being made on the balance owing.\u00a0 This is the \u2018annuity\u2019 part of the problem.\r\n\r\n&nbsp;\r\n<h2>Example 5.5.3: Deferred Repayment of Money Owed with BGN ON<\/h2>\r\nLuis is renovating his kitchen.\u00a0 He takes advantage of a promotion offered by Home Depot: \u201cPay nothing for 18 months.\u201d\u00a0 He purchases $7,500 of materials on his Home Depot card.\u00a0 Home Depot charges him 28.8% compounded monthly.\u00a0 18 months after the purchase, Luis makes his first of 6 monthly payments to pay off the credit card.\u00a0 What is the size of Luis\u2019s monthly payments?\r\n\r\nLet us first look at the timeline for this problem:\r\n\r\n<a href=\"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-content\/uploads\/sites\/971\/2020\/08\/5-5-Fig4.jpg\"><img class=\"wp-image-2576 size-full aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-content\/uploads\/sites\/971\/2020\/08\/5-5-Fig4.jpg\" alt=\"Timeline for deferred Annuity in Example 3\" width=\"95%\" \/><\/a>\r\n\r\nFrom there, fill in the exercise below to figure out the size of Luis' payments.\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Check Your Knowledge for Example 3<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n[h5p id=\"96\"]\r\n\r\nTo determine what to enter in the BAII Plus for Part 1, let's ask a few important questions:\r\n\r\n[h5p id=\"42\"]\r\n\r\n[h5p id=\"43\"]\r\n\r\nNext, enter the values for Part 1 into the BAII Plus:\r\n\r\n[h5p id=\"94\"]\r\n\r\n[h5p id=\"95\"]\r\n\r\nConclusion: Luis will owe $11,493.71 at the end of the deferral period (end of the 18 months). This amount will become the starting balance (PV<sub>2<\/sub>) in part 2.\r\n\r\nNext, let's ask some key questions on what to enter in the BAII Plus for Part 2:\r\n\r\n[h5p id=\"97\"]\r\n\r\n[h5p id=\"98\"]\r\n\r\nNext, enter the values for Part 2 into the BAII Plus:\r\n\r\n[h5p id=\"99\"]\r\n\r\n[h5p id=\"100\"]\r\n\r\nConclusion: Luis will need to make six monthly payments of $2,030.97 to pay off the credit card.\r\n\r\n<\/div>\r\n<\/div>\r\n&nbsp;\r\n<h1>Cost of Financing when Deferring Payments on a Debt<\/h1>\r\nAgain we use same interest formula:\r\n<p style=\"text-align: center\">[latex] \\begin{align*} \\textrm{Cost of Financing} &amp;= \\textrm{Money Out} - \\textrm{Money In} = \\textrm{\\$ OUT} - \\textrm{\\$ IN} \\end{align*} [\/latex]<\/p>\r\nWe need to be careful when calculating money in and money out for deferred annuities.\r\n<ul>\r\n \t<li>What is the money in ($ IN)? Only the initial amount borrowed (PV<sub>1<\/sub>) is considered money in ($ IN).<\/li>\r\n \t<li>What is the money out ($ OUT)? Only the regular payments (PMT<sub>2<\/sub>) are considered to be money out ($ OUT):<\/li>\r\n \t<li>You should note that because FV<sub>1<\/sub> is not a payment but instead becomes the starting balance for the annuity (PV<sub>2<\/sub>), it is not included in our interest calculation.<\/li>\r\n<\/ul>\r\n<table class=\"no-lines aligncenter\" style=\"border-collapse: collapse;width: 100%;height: 52px\">\r\n<thead>\r\n<tr style=\"height: 18px\">\r\n<th style=\"width: 12.5%;height: 18px\">PV<sub>1<\/sub><\/th>\r\n<th style=\"width: 12.5%;height: 18px\">Interest<sub>1<\/sub><\/th>\r\n<th style=\"width: 12.5%;height: 18px\">PMT<sub>1<\/sub><\/th>\r\n<th style=\"width: 12.5%;height: 18px\">FV<sub>1<\/sub><\/th>\r\n<th style=\"width: 12.5%;height: 18px\">PV<sub>2<\/sub><\/th>\r\n<th style=\"width: 12.5%;height: 18px\">Interest<sub>2<\/sub><\/th>\r\n<th style=\"width: 12.5%;height: 18px\">PMT<sub>2<\/sub><\/th>\r\n<th style=\"width: 12.5%;height: 18px\">FV<sub>2<\/sub><\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 12.5%;height: 16px\"><strong>Initial Deposit<\/strong><\/td>\r\n<td style=\"width: 12.5%;height: 16px\"><strong>+ % Earned<\/strong><\/td>\r\n<td style=\"width: 12.5%;height: 16px\"><strong><span style=\"color: #000000\">+ $0<\/span><\/strong><\/td>\r\n<td style=\"width: 12.5%;height: 16px\"><span style=\"color: #ff0000\"><strong>=Ending Balance Part 1<\/strong><\/span><\/td>\r\n<td style=\"width: 12.5%;height: 16px\"><strong><span style=\"color: #000000\">=Starting Balance Part 2<\/span><\/strong><\/td>\r\n<td style=\"width: 12.5%;height: 16px\"><strong>+ % Earned<\/strong><\/td>\r\n<td style=\"width: 12.5%;height: 16px\"><span style=\"color: #ff0000\"><strong>=<\/strong> <strong>Regular Payments<\/strong><\/span><\/td>\r\n<td style=\"width: 12.5%;height: 16px\"><strong><span style=\"color: #ff0000\">+ $0<\/span><\/strong><\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px\">\r\n<td style=\"width: 12.5%;height: 18px\">$ IN<\/td>\r\n<td style=\"width: 12.5%;height: 18px\">$ IN<\/td>\r\n<td style=\"width: 12.5%;height: 18px\"><strong>\u2013\u2013<\/strong><\/td>\r\n<td style=\"width: 12.5%;height: 18px\"><strong><span style=\"color: #ff0000\">\u2013\u2013<\/span><\/strong><\/td>\r\n<td style=\"width: 12.5%;height: 18px\"><strong>\u2013\u2013<\/strong><\/td>\r\n<td style=\"width: 12.5%;height: 18px\">$ IN<\/td>\r\n<td style=\"width: 12.5%;height: 18px\"><span style=\"color: #ff0000\">$ OUT<\/span><\/td>\r\n<td style=\"width: 12.5%;height: 18px\"><strong><span style=\"color: #ff0000\">\u2013\u2013<\/span><\/strong><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nThis gives us the following equation for cost of financing:\r\n<p style=\"text-align: center\">[latex]\\begin{align*}\r\n\\textrm{Cost of Financing} &amp;=\\textrm{\\$ OUT} -\\textrm{\\$ IN}\\\\\r\n&amp;=\\textrm{Regular Payments} - \\textrm{Amount Borrowed}\\\\\r\n&amp;=PMT_{2}\u00d7N_{2}-PV_{1}\r\n\\end{align*}[\/latex]<\/p>\r\n&nbsp;\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Check Your Knowledge 5.5.3<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n[h5p id=\"101\"]\r\n\r\n[h5p id=\"102\"]\r\n\r\n<\/div>\r\n<\/div>\r\n&nbsp;\r\n<h1>Deferred Repayment with the Initial Amount Owed Unknown<\/h1>\r\nIt is possible that the initial amount borrowed (PV<sub>1<\/sub>) for a deferred annuity is unknown.\r\n\r\n<a href=\"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-content\/uploads\/sites\/971\/2020\/08\/5-5-Fig6.jpg\"><img class=\"size-full wp-image-2751\" src=\"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-content\/uploads\/sites\/971\/2020\/08\/5-5-Fig6.jpg\" alt=\"Timeline for deferred annuity with initial amount unknown\" width=\"95%\" \/><\/a>\r\n\r\nIn the case, we must know the payment size in part 2 (PMT<sub>2<\/sub>). For this reason, we start with part 2 (the annuity) in these cases. See Jessa's example below where she knows the size of the monthly payments required to finance a bedroom set at Ikea.\r\n<h2>Example 5.5.4: Deferred Repayment with the Initial Amount Owed Unknown<\/h2>\r\nJessa is shopping at Ikea. She sees a sign for a beautiful bedroom furniture set. The sign reads the following. \u201cMake no payments for 6 months followed by 12 easy payments of $129.99 for this entire bedroom set.\u201d Jessa has just moved into her new apartment and needs new bedroom furniture but she\u2019s a bit tight on cash right now. She is interested in the furniture and curious about how much the actual bedroom set costs. She reads the fine-print on the sign that states that Ikea charges an effective interest rate of 28.8% on financed purchases. What is the cost of financing that Jessa will pay if she purchases the bedroom set this way?\r\n\r\nLet us first look at the timeline for this problem:\r\n\r\n<a href=\"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-content\/uploads\/sites\/971\/2020\/08\/5-5-Fig5.jpg\"><img class=\"size-full wp-image-2632\" src=\"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-content\/uploads\/sites\/971\/2020\/08\/5-5-Fig5.jpg\" alt=\"Timeline of deferred annuity for Example 4\" width=\"95%\" \/><\/a>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Check Your Knowledge 5.5.4<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nLet's find the price of the bedroom furniture set by breaking down this question into pieces. First, determine which \"part\" to start with:\r\n\r\n[h5p id=\"103\"]\r\n\r\nNext, drag and drop the correct values for Part 2 into the BAII Plus table:\r\n\r\n[h5p id=\"104\"]\r\n\r\n[h5p id=\"105\"]\r\n\r\nJessa will owe $1,373.71 when she starts making regular payments. Use this amount (and make it negative) for FV1.\r\n\r\nNext, drag and drop the correct values for Part 1 into the BAII Plus table:\r\n\r\n[h5p id=\"107\"]\r\n\r\n[h5p id=\"108\"]\r\n\r\nThe price of the furniture set is $1,191.51. Use this amount to calculate the\u00a0cost of financing that Jessa will pay on her Ikea purchase:\r\n\r\n[h5p id=\"109\"]\r\n\r\n[h5p id=\"110\"]\r\n\r\nConclusion: Jess will pay $368.37 in interest on her Ikea purchase.\r\n\r\n<\/div>\r\n<\/div>\r\n<h1>Your Own Notes<\/h1>\r\n<ul>\r\n \t<li>Are there any notes you want to take from this section? Is there anything you'd like to copy and paste below?<\/li>\r\n \t<li>These notes are for you only (they will not be stored anywhere)<\/li>\r\n \t<li>Make sure to download them at the end to use as a reference<\/li>\r\n<\/ul>\r\n[h5p id=\"1\"]\r\n<h1>The Footnotes<\/h1>","rendered":"<div class=\"textbox textbox--learning-objectives\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Outcomes<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Calculate deferred withdrawals from a retirement fund and deferred payments on a debt.<\/p>\n<\/div>\n<\/div>\n<p>To understand <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_1024_2159\">deferred annuities<\/a>, let us first go back and examine the definition of an annuity. An <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_1024_2160\">annuity<\/a> is \u201ca series of equal-sized payments, at regular intervals, over a fixed period of time.\u201d What then does it mean to defer this annuity?\u00a0 It means to delay (or defer) the regular payments for a period of time.<\/p>\n<p>Because there is a deferral period and a payment (annuity) period, there are actually two parts to the problem:<\/p>\n<p><a href=\"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-content\/uploads\/sites\/971\/2020\/08\/5-5-Fig1.jpg\"><img decoding=\"async\" class=\"wp-image-2558 size-full aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-content\/uploads\/sites\/971\/2020\/08\/5-5-Fig1.jpg\" alt=\"Timeline of a deferred annuity\" width=\"90%\" \/><\/a><\/p>\n<p><span style=\"color: #000000\"><strong>Part 1<\/strong><\/span>: Deferral Period<\/p>\n<ul>\n<li>There are no payments in part 1 (PMT<sub>1<\/sub> = 0).<\/li>\n<li>The only money being added to the initial balance (PV<sub>1<\/sub>) is the interest being earned (or charged).<\/li>\n<li>The ending balance from the deferral period (FV<sub>1<\/sub>) equals the starting balance for the annuity (PV<sub>2<\/sub>).<\/li>\n<\/ul>\n<p><span style=\"color: #000000\"><strong>Part 2<\/strong><\/span>: Annuity with Regular Payments<\/p>\n<ul>\n<li>Payments are being made or withdrawn (PMT<sub>2<\/sub>).<\/li>\n<li>Assume the final future value (FV<sub>2<\/sub>) equals 0 unless told otherwise.<\/li>\n<\/ul>\n<p>See the sections below for key formulas, tips and examples related to deferred annuities calculations.<\/p>\n<h1>Examples of Deferred Annuities<\/h1>\n<p>The most common example of a deferred annuity is a retirement fund where the investor is not yet ready to retire. They defer their withdrawals (payments) until they retire. In the mean time, the fund earns interest. The fund continues to earn interest as the investor withdraws money from the fund.<\/p>\n<p>Other possible examples of deferred annuities are student loans<a class=\"footnote\" title=\"A student loan is a special case of a deferred annuity in that if the student receives a government-sponsored student loan, they do not need to pay any interest while they are in school.\" id=\"return-footnote-1024-1\" href=\"#footnote-1024-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a> and in-store credit cards that offer \u201cpay nothing for 18 months\u201d promotions on their in-store credit cards. These are both less than perfect examples of deferred annuities in that they both come with exceptions.<\/p>\n<p>In the case of the student loan, the student defers repaying the loan until after they have finished school<a class=\"footnote\" title=\"If the Government of Canada has given out the student loan, then it is a special case of a deferred annuity. The student does indeed defer their payments until after they have finished school (they can wait up to 6 months after they are done school to start their payments).\" id=\"return-footnote-1024-2\" href=\"#footnote-1024-2\" aria-label=\"Footnote 2\"><sup class=\"footnote\">[2]<\/sup><\/a>. What is special about this case is that the Government does not charge them any interest during the deferment. If the loan is granted by a bank or other financial institution, then the student gets charged interest during the deferral period.<\/p>\n<p>In the case of \u201cpay nothing for 18 months\u201d promotion, the credit card holder defers payments (possibly waits for 18 months to start making payments) on the card. These cards and promotions come with a lot of fine print and exceptions. The credit card example becomes like a deferred annuity if the credit card holder fails to pay off the entire balance on the card before the 18 months is up. They get back-charged interest on the amount borrowed. If, after this happens, they set up a payment schedule to repay the amount owing on the card with regular, equal-sized payments, then the credit card example becomes a deferred annuity example.<\/p>\n<h1>Saving for Retirement EXAMPLES<\/h1>\n<p>If you search the web for \u2018deferred annuity\u2019 \u2014\u00a0the savings deferred annuity related to planning for retirement will come up in at least the top 5 searches. It is the most common type of deferred annuity. When people plan for their retirement, they start saving before they retire. They usually do not need to withdrawn money from a retirement fund until they retire. In other words, they defer the withdrawals until retirement. Let us look at an example of this to better understand this type of deferred annuity.<\/p>\n<p>&nbsp;<\/p>\n<h2>Example 5.5.1: Deferred Withdrawals from a Retirement Fund with BGN Off<\/h2>\n<p>Ann and Sue sell their recreation property. They make $245,000 on the sale and deposit it immediately into a retirement fund. The fund earns 2.45%, compounded monthly, for the entire time.\u00a0\u00a0 Exactly ten years after the sale, Ann retires. They now want to start supplementing their income with payments from the retirement fund. They want the payments to start one month after Ann retires.\u00a0 They want these payments to last for 5 years. How much can they withdraw per month from the retirement fund?<\/p>\n<p>Let us first organize this information into a time diagram:<\/p>\n<p><a href=\"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-content\/uploads\/sites\/971\/2020\/08\/5-5-Fig2.jpg\"><img decoding=\"async\" class=\"wp-image-2567 size-full aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-content\/uploads\/sites\/971\/2020\/08\/5-5-Fig2.jpg\" alt=\"Timeline of deferred annuity in Example 1\" width=\"95%\" \/><\/a><\/p>\n<ul>\n<li>The deferral period (part 1) occurs first.<\/li>\n<li>The deposit of $245,000 occurs at the very beginning of this deferral period.<\/li>\n<li>No payments nor withdrawals are made for the first 10 years (only interest is added for these 10 years).<\/li>\n<li>After the 10 years is complete, part 2, the annuity, begins.<\/li>\n<li>One month after the start of part 2 (annuity), the first withdrawal occurs.<\/li>\n<li>These withdrawals repeat for 5 years until no money is left in the annuity.<\/li>\n<\/ul>\n<p>The tricky part with these types of problems with two parts is determining which part to start with. Start where the &#8220;known&#8221; money is. In this example, we know that Ann and Sue deposit $245,000 immediately (PV<sub>1<\/sub> = 245,000). For this reason, we will start with part 1 because PV<sub>1<\/sub> is known.<\/p>\n<p><span style=\"color: #000000\"><strong>Part 1<\/strong><\/span>: Let us now organize the information for Part 1 into a BAII Plus table:<\/p>\n<table class=\"lines aligncenter\" style=\"border-collapse: collapse;width: 90%\">\n<thead>\n<tr>\n<th class=\"border\" style=\"width: 8%\">B\/E<\/th>\n<th class=\"border\" style=\"width: 8%\">P\/Y<\/th>\n<th class=\"border\" style=\"width: 8%\">C\/Y<\/th>\n<th class=\"border\" style=\"width: 20%\">N<sub>1<\/sub><\/th>\n<th class=\"border\" style=\"width: 8%\">I\/Y<\/th>\n<th class=\"border\" style=\"width: 12%\">PV<sub>1<\/sub><\/th>\n<th class=\"border\" style=\"width: 8%\">PMT<sub>1<\/sub><\/th>\n<th class=\"border\" style=\"width: 28%\">FV<sub>1<\/sub><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td class=\"border\" style=\"width: 8%\">\u2013\u2013<\/td>\n<td class=\"border\" style=\"width: 8%\">12<\/td>\n<td class=\"border\" style=\"width: 8%\">12<\/td>\n<td class=\"border\" style=\"width: 20%\">10\u00d712=120<\/td>\n<td class=\"border\" style=\"width: 8%\">2.45<\/td>\n<td class=\"border\" style=\"width: 12%\">+245,000<\/td>\n<td class=\"border\" style=\"width: 8%\">0<\/td>\n<td class=\"border\" style=\"width: 28%\"><strong>CPT<\/strong> <span style=\"color: #ff0000\">-312,939.05<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<ul>\n<li>Since there are no payments, B\/E doesn&#8217;t matter (that is why &#8216;<a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_1024_3272\">\u2013\u2013<\/a>&#8216; <strong>\u00a0<\/strong>is set for B\/E).<\/li>\n<li>Because the interest rate is 2.45% compounding monthly, I\/Y = 2.45 and C\/Y = 12.<\/li>\n<li>Because there are no payments, match P\/Y to C\/Y (P\/Y = 12).<\/li>\n<li>The deferral period lasts 10 years, so N<sub>1<\/sub> = 10\u00d712=120.<\/li>\n<li>Remember, the $245,000 deposit occurs at the very beginning so PV<sub>1 <\/sub>= +245,000.<\/li>\n<li>There are no payments for the deferral period so PMT<sub>1<\/sub> = 0.<\/li>\n<li><strong>CPT<\/strong> \u00a0FV<sub>1 <\/sub>= \u2212312,939.05. Ann and Sue&#8217;s initial deposit grows to $312,939.05 after 10 years due to the interest earned on the deposit.<\/li>\n<li>The $312,939.05 (FV<sub>1<\/sub>) will become the starting value for the annuity in part 2 (PV<sub>2<\/sub>).<\/li>\n<\/ul>\n<p><span style=\"color: #000000\"><strong>Part 2<\/strong><\/span>: Let us now organize the information for Part 2 into a BAII Plus table:<\/p>\n<table class=\"lines aligncenter\" style=\"border-collapse: collapse;width: 90%\">\n<thead>\n<tr>\n<th class=\"border\" style=\"width: 8%\">B\/E<\/th>\n<th class=\"border\" style=\"width: 8%\">P\/Y<\/th>\n<th class=\"border\" style=\"width: 8%\">C\/Y<\/th>\n<th class=\"border\" style=\"width: 20%\">N<sub>2<\/sub><\/th>\n<th class=\"border\" style=\"width: 8%\">I\/Y<\/th>\n<th class=\"border\" style=\"width: 12%\">PV<sub>2<\/sub><\/th>\n<th class=\"border\" style=\"width: 28%\">PMT<sub>2<\/sub><\/th>\n<th class=\"border\" style=\"width: 8%\">FV<sub>2<\/sub><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td class=\"border\" style=\"width: 8%\">END<\/td>\n<td class=\"border\" style=\"width: 8%\">12<\/td>\n<td class=\"border\" style=\"width: 8%\">12<\/td>\n<td class=\"border\" style=\"width: 20%\">5\u00d712=60<\/td>\n<td class=\"border\" style=\"width: 8%\">2.45<\/td>\n<td class=\"border\" style=\"width: 12%\">+312,939.05<\/td>\n<td class=\"border\" style=\"width: 28%\"><strong>CPT<\/strong> <span style=\"color: #ff0000\">\u22125,546.95<\/span><\/td>\n<td class=\"border\" style=\"width: 8%\">0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<ul>\n<li>The payments start one month after Ann retires (in one payment interval), so B\/E = <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_1024_2089\">END<\/a>.<\/li>\n<li>Because the interest rate is still 2.45% compounding monthly, I\/Y = 2.45 and C\/Y = 12.<\/li>\n<li>Ann and Sue receive monthly payments so P\/Y = 12.<\/li>\n<li>They want these payments to last 5 years so, N<sub>2<\/sub> = 5\u00d712=60.<\/li>\n<li>Use the (positive) value of FV<sub>1<\/sub> for PV<sub>2<\/sub>. So, PV2 = +<span style=\"color: #000000\">312,939.05<\/span>.<\/li>\n<li>There is no money left at the end of 5 years so FV<sub>2<\/sub> = 0.<\/li>\n<li>Compute PMT<sub>2<\/sub> to get the size of Ann and Sue&#8217;s monthly withdrawals.<\/li>\n<\/ul>\n<p>Conclusion: Ann and Sue can withdraw $5,546.95 per month from their retirement fund.<\/p>\n<p>&nbsp;<\/p>\n<h2>Example 5.5.2: Deferred Withdrawals from a Retirement Fund with BGN On<\/h2>\n<p>What would change in Example 1 if Ann and Sue made the first withdrawal exactly 10 years after the sale of their property?\u00a0 Ie: what if their first withdrawal occurred the day that Ann retired?<\/p>\n<p>Let us first look at the timeline for this problem:<\/p>\n<p><a href=\"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-content\/uploads\/sites\/971\/2020\/08\/5-5-Fig3.jpg\"><img decoding=\"async\" class=\"wp-image-2571 size-full aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-content\/uploads\/sites\/971\/2020\/08\/5-5-Fig3.jpg\" alt=\"Timeline of deferred annuity for Example 2\" width=\"95%\" \/><\/a><\/p>\n<ul>\n<li><span style=\"color: #000000\"><strong>Part 1 <\/strong><\/span>is the same as in Example 1, so we do not need to redo those calculations.<\/li>\n<li><span style=\"color: #000000\"><strong>Part 2<\/strong><\/span> has changed. The first withdrawal (PMT<sub>2<\/sub>) now occurs exactly at the start (beginning) of that annuity.<\/li>\n<li>This means we set the calculator to <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_1024_2088\">BGN<\/a> when calculating the annuity payments in part 2 (PMT<sub>2<\/sub>):<\/li>\n<\/ul>\n<table class=\"lines aligncenter\" style=\"border-collapse: collapse;width: 90%\">\n<thead>\n<tr>\n<th class=\"border\" style=\"width: 8%\">B\/E<\/th>\n<th class=\"border\" style=\"width: 8%\">P\/Y<\/th>\n<th class=\"border\" style=\"width: 8%\">C\/Y<\/th>\n<th class=\"border\" style=\"width: 20%\">N<sub>2<\/sub><\/th>\n<th class=\"border\" style=\"width: 8%\">I\/Y<\/th>\n<th class=\"border\" style=\"width: 12%\">PV<sub>2<\/sub><\/th>\n<th class=\"border\" style=\"width: 28%\">PMT<sub>2<\/sub><\/th>\n<th class=\"border\" style=\"width: 8%\">FV<sub>2<\/sub><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td class=\"border\" style=\"width: 8%\">END<\/td>\n<td class=\"border\" style=\"width: 8%\">12<\/td>\n<td class=\"border\" style=\"width: 8%\">12<\/td>\n<td class=\"border\" style=\"width: 20%\">5\u00d712=60<\/td>\n<td class=\"border\" style=\"width: 8%\">2.45<\/td>\n<td class=\"border\" style=\"width: 12%\">+312,939.05<\/td>\n<td class=\"border\" style=\"width: 28%\"><strong>CPT<\/strong> <span style=\"color: #ff0000\">\u22125,535.64<\/span><\/td>\n<td class=\"border\" style=\"width: 8%\">0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h4>Conclusions:<\/h4>\n<ul>\n<li>The amount withdrawn by Ann and Sue decreases slightly from $5,546.95 to $5,535.64 when they make the first withdrawal on the day that Ann retires.<\/li>\n<li>Withdrawing the first payment one month earlier means that Ann and Sue will miss out on the interest that would have been earned on that payment.<\/li>\n<li>This is because the money in the annuity continues to earn interest as the withdrawals are being made.<\/li>\n<li>As a result, Sue and Ann withdraw $11.31 less per month if they make the first withdrawal exactly 10 years after the sale of their property.<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h1>Interest Earned when Saving for Retirement<\/h1>\n<p>Again we use same interest formula:<\/p>\n<p style=\"text-align: center\">[latex]\\begin{align*} \\textrm{Interest Earned} &= \\textrm{Money Out} - \\textrm{Money In} = \\textrm{\\$ OUT} - \\textrm{\\$ IN} \\end{align*}[\/latex]<\/p>\n<p>We need to be careful when calculating money in and money out for deferred annuities.<\/p>\n<ul>\n<li>What money was deposited in the account? Only the initial deposit (PV<sub>1<\/sub>) is considered money in ($ IN).<\/li>\n<li>What money do we take out (withdraw)? Only the regular withdrawals (PMT<sub>2<\/sub>) and final withdrawal (FV<sub>2<\/sub>) in part 2 are considered to be money out ($ OUT).<\/li>\n<li>Because FV<sub>1<\/sub> does not get withdrawn but instead becomes the starting balance for the annuity (PV<sub>2<\/sub>), it is not included in our interest calculation. The money is neither being deposited nor withdrawn.<\/li>\n<\/ul>\n<table class=\"no-lines aligncenter\" style=\"border-collapse: collapse;width: 100%;height: 52px\">\n<thead>\n<tr style=\"height: 18px\">\n<th style=\"width: 12.5%;height: 18px\">PV<sub>1<\/sub><\/th>\n<th style=\"width: 12.5%;height: 18px\">Interest<sub>1<\/sub><\/th>\n<th style=\"width: 12.5%;height: 18px\">PMT<sub>1<\/sub><\/th>\n<th style=\"width: 12.5%;height: 18px\">FV<sub>1<\/sub><\/th>\n<th style=\"width: 12.5%;height: 18px\">PV<sub>2<\/sub><\/th>\n<th style=\"width: 12.5%;height: 18px\">Interest<sub>2<\/sub><\/th>\n<th style=\"width: 12.5%;height: 18px\">PMT<sub>2<\/sub><\/th>\n<th style=\"width: 12.5%;height: 18px\">FV<sub>2<\/sub><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr style=\"height: 16px\">\n<td style=\"width: 12.5%;height: 16px\"><strong>Initial Deposit<\/strong><\/td>\n<td style=\"width: 12.5%;height: 16px\"><strong>+ % Earned<\/strong><\/td>\n<td style=\"width: 12.5%;height: 16px\"><strong><span style=\"color: #000000\">+ $0<\/span><\/strong><\/td>\n<td style=\"width: 12.5%;height: 16px\"><span style=\"color: #ff0000\"><strong>=Ending Balance Part 1<\/strong><\/span><\/td>\n<td style=\"width: 12.5%;height: 16px\"><strong><span style=\"color: #000000\">=Starting Balance Part 2<\/span><\/strong><\/td>\n<td style=\"width: 12.5%;height: 16px\"><strong>+ % Earned<\/strong><\/td>\n<td style=\"width: 12.5%;height: 16px\"><span style=\"color: #ff0000\"><strong>=<\/strong> <strong>Regular Withdrawals<\/strong><\/span><\/td>\n<td style=\"width: 12.5%;height: 16px\"><strong><span style=\"color: #ff0000\">+ Final<\/span><span style=\"color: #ff0000\"> Wit<\/span><span style=\"color: #ff0000\">hdraw<\/span><span style=\"color: #ff0000\">al<\/span><\/strong><\/td>\n<\/tr>\n<tr style=\"height: 18px\">\n<td style=\"width: 12.5%;height: 18px\">$ IN<\/td>\n<td style=\"width: 12.5%;height: 18px\">$ IN<\/td>\n<td style=\"width: 12.5%;height: 18px\"><strong>\u2013\u2013<\/strong><\/td>\n<td style=\"width: 12.5%;height: 18px\"><strong><span style=\"color: #ff0000\">\u2013\u2013<\/span><\/strong><\/td>\n<td style=\"width: 12.5%;height: 18px\"><strong>\u2013\u2013<\/strong><\/td>\n<td style=\"width: 12.5%;height: 18px\">$ IN<\/td>\n<td style=\"width: 12.5%;height: 18px\"><span style=\"color: #ff0000\">$ OUT<\/span><\/td>\n<td style=\"width: 12.5%;height: 18px\"><span style=\"color: #ff0000\">$ OUT<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>This gives us the following equation for interest earned:<\/p>\n<p style=\"text-align: center\">[latex]\\begin{align*} \\textrm{Interest Earned} &= \\textrm{\\$ OUT} - \\textrm{\\$ IN}\\\\ &=( \\textrm{Regular Withdrawals}+\\textrm{Final Withdrawal}) - \\textrm{Initial Deposit}\\\\ &= ( \\textrm{PMT}_2\\times\\textrm{N}_2+\\textrm{FV}_2)-\\textrm{PV}_1 \\end{align*}[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Check Your Knowledge 5.5.0<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Calculate the amount of interest Ann and Sue will earn in on their retirement savings plan from Example 2:<\/p>\n<div id=\"h5p-92\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-92\" class=\"h5p-iframe\" data-content-id=\"92\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"5.5.0 Calculating Interest\"><\/iframe><\/div>\n<\/div>\n<div id=\"h5p-93\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-93\" class=\"h5p-iframe\" data-content-id=\"93\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"5.5.0 Calculating Interest Answers\"><\/iframe><\/div>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<h1>Deferring Payments on a Debt EXAMPLE &amp; Key Takeaways<\/h1>\n<p>It is quite common to defer payments when purchasing items, especially in retail.\u00a0 A retailer purchases their goods from a supplier.\u00a0 If cash flow is an issue for the retailer, they can often choose to defer the payments on the shipment until a later date.\u00a0 It is also common when consumers purchase items using \u201cin-store\u201d credit cards.\u00a0 Some stores have \u201cPay Nothing\u201d promotions for their customers.\u00a0 If a customer purchases goods from the store on the in-store credit card, they can choose to make no payments on their purchase for a certain amount of time (6 months, 12 months, 18 months,\u2026).<\/p>\n<p>In the above cases, the retailer or customer owes the value of the amount of goods they purchased.\u00a0 They make no payments for a certain amount of time (they defer their payments).\u00a0 After the deferral period has passed, they make payments to repay the value of the goods plus the interest charged during the deferral period.\u00a0 See the timeline describing this process:<\/p>\n<p><a href=\"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-content\/uploads\/sites\/971\/2020\/08\/5-5-Fig1-1.jpg\"><img decoding=\"async\" class=\"wp-image-2562 size-full aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-content\/uploads\/sites\/971\/2020\/08\/5-5-Fig1-1.jpg\" alt=\"Timeline of a deferred annuity\" width=\"90%\" \/><\/a><\/p>\n<p><strong>Part 1<\/strong>: The initial amount owing gathers interest.\u00a0 There are no payments in part 1 (the deferral period).\u00a0 The only money being added to the balance is the interest being charged.\u00a0 This problem is a compound interest problem (Chapter 4):<\/p>\n<p><strong>Part 2<\/strong>: Payments are now being made on the balance owing.\u00a0 This is the \u2018annuity\u2019 part of the problem.<\/p>\n<p>&nbsp;<\/p>\n<h2>Example 5.5.3: Deferred Repayment of Money Owed with BGN ON<\/h2>\n<p>Luis is renovating his kitchen.\u00a0 He takes advantage of a promotion offered by Home Depot: \u201cPay nothing for 18 months.\u201d\u00a0 He purchases $7,500 of materials on his Home Depot card.\u00a0 Home Depot charges him 28.8% compounded monthly.\u00a0 18 months after the purchase, Luis makes his first of 6 monthly payments to pay off the credit card.\u00a0 What is the size of Luis\u2019s monthly payments?<\/p>\n<p>Let us first look at the timeline for this problem:<\/p>\n<p><a href=\"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-content\/uploads\/sites\/971\/2020\/08\/5-5-Fig4.jpg\"><img decoding=\"async\" class=\"wp-image-2576 size-full aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-content\/uploads\/sites\/971\/2020\/08\/5-5-Fig4.jpg\" alt=\"Timeline for deferred Annuity in Example 3\" width=\"95%\" \/><\/a><\/p>\n<p>From there, fill in the exercise below to figure out the size of Luis&#8217; payments.<\/p>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Check Your Knowledge for Example 3<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"h5p-96\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-96\" class=\"h5p-iframe\" data-content-id=\"96\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"5.5.1 Which part to start with?\"><\/iframe><\/div>\n<\/div>\n<p>To determine what to enter in the BAII Plus for Part 1, let&#8217;s ask a few important questions:<\/p>\n<div id=\"h5p-42\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-42\" class=\"h5p-iframe\" data-content-id=\"42\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"5.5.1 Key Takeaways for the Deferral Period\"><\/iframe><\/div>\n<\/div>\n<div id=\"h5p-43\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-43\" class=\"h5p-iframe\" data-content-id=\"43\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"5.5.1 Key Takeaways for the Deferral Period Answers\"><\/iframe><\/div>\n<\/div>\n<p>Next, enter the values for Part 1 into the BAII Plus:<\/p>\n<div id=\"h5p-94\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-94\" class=\"h5p-iframe\" data-content-id=\"94\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"5.5.1 Correct values for Part 1 into the BAII Plus table\"><\/iframe><\/div>\n<\/div>\n<div id=\"h5p-95\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-95\" class=\"h5p-iframe\" data-content-id=\"95\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"5.5.1 Correct values for Part 1 into the BAII Plus table Answers\"><\/iframe><\/div>\n<\/div>\n<p>Conclusion: Luis will owe $11,493.71 at the end of the deferral period (end of the 18 months). This amount will become the starting balance (PV<sub>2<\/sub>) in part 2.<\/p>\n<p>Next, let&#8217;s ask some key questions on what to enter in the BAII Plus for Part 2:<\/p>\n<div id=\"h5p-97\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-97\" class=\"h5p-iframe\" data-content-id=\"97\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"5.5.1 Key Questions for Part 2\"><\/iframe><\/div>\n<\/div>\n<div id=\"h5p-98\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-98\" class=\"h5p-iframe\" data-content-id=\"98\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"5.5.1 Key Questions for Part 2 Answers\"><\/iframe><\/div>\n<\/div>\n<p>Next, enter the values for Part 2 into the BAII Plus:<\/p>\n<div id=\"h5p-99\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-99\" class=\"h5p-iframe\" data-content-id=\"99\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"5.5.1 Correct values for Part 2 into the BAII Plus table\"><\/iframe><\/div>\n<\/div>\n<div id=\"h5p-100\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-100\" class=\"h5p-iframe\" data-content-id=\"100\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"5.5.1 Correct values for Part 2 into the BAII Plus table Answers\"><\/iframe><\/div>\n<\/div>\n<p>Conclusion: Luis will need to make six monthly payments of $2,030.97 to pay off the credit card.<\/p>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<h1>Cost of Financing when Deferring Payments on a Debt<\/h1>\n<p>Again we use same interest formula:<\/p>\n<p style=\"text-align: center\">[latex]\\begin{align*} \\textrm{Cost of Financing} &= \\textrm{Money Out} - \\textrm{Money In} = \\textrm{\\$ OUT} - \\textrm{\\$ IN} \\end{align*}[\/latex]<\/p>\n<p>We need to be careful when calculating money in and money out for deferred annuities.<\/p>\n<ul>\n<li>What is the money in ($ IN)? Only the initial amount borrowed (PV<sub>1<\/sub>) is considered money in ($ IN).<\/li>\n<li>What is the money out ($ OUT)? Only the regular payments (PMT<sub>2<\/sub>) are considered to be money out ($ OUT):<\/li>\n<li>You should note that because FV<sub>1<\/sub> is not a payment but instead becomes the starting balance for the annuity (PV<sub>2<\/sub>), it is not included in our interest calculation.<\/li>\n<\/ul>\n<table class=\"no-lines aligncenter\" style=\"border-collapse: collapse;width: 100%;height: 52px\">\n<thead>\n<tr style=\"height: 18px\">\n<th style=\"width: 12.5%;height: 18px\">PV<sub>1<\/sub><\/th>\n<th style=\"width: 12.5%;height: 18px\">Interest<sub>1<\/sub><\/th>\n<th style=\"width: 12.5%;height: 18px\">PMT<sub>1<\/sub><\/th>\n<th style=\"width: 12.5%;height: 18px\">FV<sub>1<\/sub><\/th>\n<th style=\"width: 12.5%;height: 18px\">PV<sub>2<\/sub><\/th>\n<th style=\"width: 12.5%;height: 18px\">Interest<sub>2<\/sub><\/th>\n<th style=\"width: 12.5%;height: 18px\">PMT<sub>2<\/sub><\/th>\n<th style=\"width: 12.5%;height: 18px\">FV<sub>2<\/sub><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr style=\"height: 16px\">\n<td style=\"width: 12.5%;height: 16px\"><strong>Initial Deposit<\/strong><\/td>\n<td style=\"width: 12.5%;height: 16px\"><strong>+ % Earned<\/strong><\/td>\n<td style=\"width: 12.5%;height: 16px\"><strong><span style=\"color: #000000\">+ $0<\/span><\/strong><\/td>\n<td style=\"width: 12.5%;height: 16px\"><span style=\"color: #ff0000\"><strong>=Ending Balance Part 1<\/strong><\/span><\/td>\n<td style=\"width: 12.5%;height: 16px\"><strong><span style=\"color: #000000\">=Starting Balance Part 2<\/span><\/strong><\/td>\n<td style=\"width: 12.5%;height: 16px\"><strong>+ % Earned<\/strong><\/td>\n<td style=\"width: 12.5%;height: 16px\"><span style=\"color: #ff0000\"><strong>=<\/strong> <strong>Regular Payments<\/strong><\/span><\/td>\n<td style=\"width: 12.5%;height: 16px\"><strong><span style=\"color: #ff0000\">+ $0<\/span><\/strong><\/td>\n<\/tr>\n<tr style=\"height: 18px\">\n<td style=\"width: 12.5%;height: 18px\">$ IN<\/td>\n<td style=\"width: 12.5%;height: 18px\">$ IN<\/td>\n<td style=\"width: 12.5%;height: 18px\"><strong>\u2013\u2013<\/strong><\/td>\n<td style=\"width: 12.5%;height: 18px\"><strong><span style=\"color: #ff0000\">\u2013\u2013<\/span><\/strong><\/td>\n<td style=\"width: 12.5%;height: 18px\"><strong>\u2013\u2013<\/strong><\/td>\n<td style=\"width: 12.5%;height: 18px\">$ IN<\/td>\n<td style=\"width: 12.5%;height: 18px\"><span style=\"color: #ff0000\">$ OUT<\/span><\/td>\n<td style=\"width: 12.5%;height: 18px\"><strong><span style=\"color: #ff0000\">\u2013\u2013<\/span><\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>This gives us the following equation for cost of financing:<\/p>\n<p style=\"text-align: center\">[latex]\\begin{align*}  \\textrm{Cost of Financing} &=\\textrm{\\$ OUT} -\\textrm{\\$ IN}\\\\  &=\\textrm{Regular Payments} - \\textrm{Amount Borrowed}\\\\  &=PMT_{2}\u00d7N_{2}-PV_{1}  \\end{align*}[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Check Your Knowledge 5.5.3<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"h5p-101\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-101\" class=\"h5p-iframe\" data-content-id=\"101\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"5.5.3 Cost of Financing Calculation\"><\/iframe><\/div>\n<\/div>\n<div id=\"h5p-102\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-102\" class=\"h5p-iframe\" data-content-id=\"102\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"5.5.3 Cost of Financing Calculation Answer\"><\/iframe><\/div>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<h1>Deferred Repayment with the Initial Amount Owed Unknown<\/h1>\n<p>It is possible that the initial amount borrowed (PV<sub>1<\/sub>) for a deferred annuity is unknown.<\/p>\n<p><a href=\"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-content\/uploads\/sites\/971\/2020\/08\/5-5-Fig6.jpg\"><img decoding=\"async\" class=\"size-full wp-image-2751\" src=\"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-content\/uploads\/sites\/971\/2020\/08\/5-5-Fig6.jpg\" alt=\"Timeline for deferred annuity with initial amount unknown\" width=\"95%\" \/><\/a><\/p>\n<p>In the case, we must know the payment size in part 2 (PMT<sub>2<\/sub>). For this reason, we start with part 2 (the annuity) in these cases. See Jessa&#8217;s example below where she knows the size of the monthly payments required to finance a bedroom set at Ikea.<\/p>\n<h2>Example 5.5.4: Deferred Repayment with the Initial Amount Owed Unknown<\/h2>\n<p>Jessa is shopping at Ikea. She sees a sign for a beautiful bedroom furniture set. The sign reads the following. \u201cMake no payments for 6 months followed by 12 easy payments of $129.99 for this entire bedroom set.\u201d Jessa has just moved into her new apartment and needs new bedroom furniture but she\u2019s a bit tight on cash right now. She is interested in the furniture and curious about how much the actual bedroom set costs. She reads the fine-print on the sign that states that Ikea charges an effective interest rate of 28.8% on financed purchases. What is the cost of financing that Jessa will pay if she purchases the bedroom set this way?<\/p>\n<p>Let us first look at the timeline for this problem:<\/p>\n<p><a href=\"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-content\/uploads\/sites\/971\/2020\/08\/5-5-Fig5.jpg\"><img decoding=\"async\" class=\"size-full wp-image-2632\" src=\"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-content\/uploads\/sites\/971\/2020\/08\/5-5-Fig5.jpg\" alt=\"Timeline of deferred annuity for Example 4\" width=\"95%\" \/><\/a><\/p>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Check Your Knowledge 5.5.4<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Let&#8217;s find the price of the bedroom furniture set by breaking down this question into pieces. First, determine which &#8220;part&#8221; to start with:<\/p>\n<div id=\"h5p-103\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-103\" class=\"h5p-iframe\" data-content-id=\"103\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"5.5.4 Which part to start with?\"><\/iframe><\/div>\n<\/div>\n<p>Next, drag and drop the correct values for Part 2 into the BAII Plus table:<\/p>\n<div id=\"h5p-104\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-104\" class=\"h5p-iframe\" data-content-id=\"104\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"5.5.4 Correct values for Part 2 into the BAII Plus table\"><\/iframe><\/div>\n<\/div>\n<div id=\"h5p-105\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-105\" class=\"h5p-iframe\" data-content-id=\"105\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"5.5.4 Correct values for Part 2 into the BAII Plus table Answers\"><\/iframe><\/div>\n<\/div>\n<p>Jessa will owe $1,373.71 when she starts making regular payments. Use this amount (and make it negative) for FV1.<\/p>\n<p>Next, drag and drop the correct values for Part 1 into the BAII Plus table:<\/p>\n<div id=\"h5p-107\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-107\" class=\"h5p-iframe\" data-content-id=\"107\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"5.5.4 Correct values for Part 1 into the BAII Plus table\"><\/iframe><\/div>\n<\/div>\n<div id=\"h5p-108\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-108\" class=\"h5p-iframe\" data-content-id=\"108\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"5.5.4 Correct values for Part 1 into the BAII Plus table Answers\"><\/iframe><\/div>\n<\/div>\n<p>The price of the furniture set is $1,191.51. Use this amount to calculate the\u00a0cost of financing that Jessa will pay on her Ikea purchase:<\/p>\n<div id=\"h5p-109\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-109\" class=\"h5p-iframe\" data-content-id=\"109\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"5.5.4 Cost of Financing Calculation\"><\/iframe><\/div>\n<\/div>\n<div id=\"h5p-110\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-110\" class=\"h5p-iframe\" data-content-id=\"110\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"5.5.4 Cost of Financing Calculation Answers\"><\/iframe><\/div>\n<\/div>\n<p>Conclusion: Jess will pay $368.37 in interest on her Ikea purchase.<\/p>\n<\/div>\n<\/div>\n<h1>Your Own Notes<\/h1>\n<ul>\n<li>Are there any notes you want to take from this section? Is there anything you&#8217;d like to copy and paste below?<\/li>\n<li>These notes are for you only (they will not be stored anywhere)<\/li>\n<li>Make sure to download them at the end to use as a reference<\/li>\n<\/ul>\n<div id=\"h5p-1\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-1\" class=\"h5p-iframe\" data-content-id=\"1\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"Key takeaways, notes and comments from this section document tool.\"><\/iframe><\/div>\n<\/div>\n<h1>The Footnotes<\/h1>\n<hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-1024-1\">A student loan is a special case of a deferred annuity in that if the student receives a government-sponsored student loan, they do not need to pay any interest while they are in school. <a href=\"#return-footnote-1024-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><li id=\"footnote-1024-2\">If the Government of Canada has given out the student loan, then it is a special case of a deferred annuity. The student does indeed defer their payments until after they have finished school (they can wait up to 6 months after they are done school to start their payments). <a href=\"#return-footnote-1024-2\" class=\"return-footnote\" aria-label=\"Return to footnote 2\">&crarr;<\/a><\/li><\/ol><\/div><div class=\"glossary\"><span class=\"screen-reader-text\" id=\"definition\">definition<\/span><template id=\"term_1024_2159\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_1024_2159\"><div tabindex=\"-1\"><p>An annuity where the regular payments are delayed for a period of time.<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_1024_2160\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_1024_2160\"><div tabindex=\"-1\"><p>A series of equal-sized payments, at regular intervals, over a fixed period of time.<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_1024_3272\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_1024_3272\"><div tabindex=\"-1\"><p>Double dash (double en dash) is used in this textbook to denote 'N\/A' or nothing needs to be entered.<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_1024_2089\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_1024_2089\"><div tabindex=\"-1\"><p>The setting in the BAII Plus to make the payments occur at the end of the payment interval.<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_1024_2088\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_1024_2088\"><div tabindex=\"-1\"><p>The setting in the BAII Plus to turn on when payments occur at the beginning of the payment interval.<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><\/div>","protected":false},"author":883,"menu_order":5,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1024","chapter","type-chapter","status-publish","hentry"],"part":46,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/pressbooks\/v2\/chapters\/1024","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/wp\/v2\/users\/883"}],"version-history":[{"count":26,"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/pressbooks\/v2\/chapters\/1024\/revisions"}],"predecessor-version":[{"id":3875,"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/pressbooks\/v2\/chapters\/1024\/revisions\/3875"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/pressbooks\/v2\/parts\/46"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/pressbooks\/v2\/chapters\/1024\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/wp\/v2\/media?parent=1024"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/pressbooks\/v2\/chapter-type?post=1024"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/wp\/v2\/contributor?post=1024"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/wp\/v2\/license?post=1024"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}