{"id":2083,"date":"2021-06-09T12:14:09","date_gmt":"2021-06-09T16:14:09","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/?post_type=chapter&#038;p=2083"},"modified":"2021-07-10T13:59:33","modified_gmt":"2021-07-10T17:59:33","slug":"annuities-due-and-leases","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/chapter\/annuities-due-and-leases\/","title":{"raw":"5.4 Leases and Annuities Due","rendered":"5.4 Leases and Annuities Due"},"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 the rate and cost of financing for car leases and understand annuities due.\r\n\r\n<\/div>\r\n<\/div>\r\nLeasing a car (or vehicle) is much like renting a vehicle. The [pb_glossary id=\"2128\"]lessee[\/pb_glossary] (person leasing the car) makes a series of equal-sized payments ([pb_glossary id=\"2129\"]lease payments[\/pb_glossary]), at regular intervals over the course of a fixed time period ([pb_glossary id=\"2130\"]lease period[\/pb_glossary]). These payments will be smaller than loan payments. This is because at the end of the lease, the lessee either must pay an additional amount called the [pb_glossary id=\"2131\"]residual value[\/pb_glossary] to purchase the car or they must return the car to the car dealership. To calculate any of the above values, we enter the following in for each value:\r\n<table class=\"no-lines aligncenter\" style=\"border-collapse: collapse;width: 80%;height: 51px\" border=\"0\">\r\n<thead>\r\n<tr style=\"height: 18px\">\r\n<th style=\"width: 24%;height: 19px\">PV<\/th>\r\n<th style=\"width: 22%;height: 19px\">Interest<\/th>\r\n<th style=\"width: 26%;height: 19px\">PMT<\/th>\r\n<th style=\"width: 28%;height: 19px\">FV<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 24%;height: 16px\"><strong>Amount Leased<\/strong><\/td>\r\n<td style=\"width: 22%;height: 16px\"><strong>+\u00a0 %Charged<\/strong><\/td>\r\n<td style=\"width: 26%;height: 16px\"><span style=\"color: #ff0000\"><strong>=\u00a0 \u00a0Lease Payments<\/strong><\/span><\/td>\r\n<td style=\"width: 28%;height: 16px\"><span style=\"color: #ff0000\"><strong>+\u00a0 \u00a0Residual Value<\/strong><\/span><\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 24%;height: 16px\"><strong><span style=\"font-size: 124%\">+<\/span><\/strong><\/td>\r\n<td style=\"width: 22%;height: 16px\"><strong><span style=\"font-size: 124%\">+<\/span><\/strong><\/td>\r\n<td style=\"width: 26%;height: 16px\"><strong><span style=\"color: #ff0000;font-size: 124%\">\u2212<\/span><\/strong><\/td>\r\n<td style=\"width: 28%;height: 16px\"><strong><span style=\"color: #ff0000;font-size: 124%\">\u2212<\/span><\/strong><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nLeases are examples of [pb_glossary id=\"985\"]annuities due[\/pb_glossary]. We will examine this term in the section below.\r\n\r\nSee the sections below for key formulas, tips and examples related to leases and annuities due.\r\n<h1>Ordinary Annuities vs Annuities Due<\/h1>\r\nWhen calculating an [pb_glossary id=\"892\"]ordinary annuity[\/pb_glossary] (an annuity where the payments occur at the end of each payment interval), you do not likely need to change anything in your calculator. By default, your calculator will be set to [pb_glossary id=\"2089\"]END[\/pb_glossary] mode (which is the setting you need for ordinary annuities).\r\n\r\nIt is also possible that payments occur at the beginning of each interval. In this case, you need to \u201ctell\u201d your calculator that the payments are occurring at the beginning of the payment interval. You do this by setting the calculator to [pb_glossary id=\"2088\"]BGN[\/pb_glossary] mode. This type of annuity is called an annuity due.\r\n<h1>How Do We SWITCH between Bgn and end on the BAII Plus?<\/h1>\r\n<h2>How Do We Set the BAII Plus to BGN?<\/h2>\r\n<ul>\r\n \t<li>Hit [pb_glossary id=\"2104\"][2ND][\/pb_glossary] followed by [pb_glossary id=\"2105\"][PMT][\/pb_glossary] on your calculator (this gets you into the BGN\/END menu).<\/li>\r\n \t<li>You will see END displayed on the screen. To change this to BGN, click on [<strong>2ND<\/strong>] and [pb_glossary id=\"2106\"][ENTER][\/pb_glossary]<\/li>\r\n \t<li>You will now see BGN displayed on the screen as well as in the top right of the screen.<\/li>\r\n \t<li>Hit [<strong>2ND<\/strong>] followed by [pb_glossary id=\"2117\"][CPT][\/pb_glossary] to exit the BGN\/END menu.<\/li>\r\n \t<li><strong>Be careful!<\/strong>\u00a0 Ordinary annuities are more common that annuities due so once you have completed your annuity due question, turn off BGN (ie: set your calculator back to END).<\/li>\r\n<\/ul>\r\n<h2>How Do We Set the BAII Plus to END?<\/h2>\r\n<ul>\r\n \t<li>Hit [<strong>2ND<\/strong>] followed by [<strong>PMT<\/strong>] on your calculator.<\/li>\r\n \t<li>You will see BGN displayed on the screen. To change this to END, click on [<strong>2ND<\/strong>] and [<strong>ENTER<\/strong>].<\/li>\r\n \t<li>You will now see END displayed on the screen and you will see BGN disappear from the top right of the calculator screen.<\/li>\r\n \t<li>Hit [<strong>2ND<\/strong>] followed by [<strong>CPT<\/strong>] to exit the BGN\/END menu.<\/li>\r\n<\/ul>\r\nNow, you can practice these steps in the exercise below.\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Check Your Knowledge 5.4.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nDrag the keys onto the calculator screen in the correct order to switch from END to BGN.\r\n\r\n[h5p id=\"33\"]\r\n\r\nDrag the keys onto the calculator screen in the correct order to switch from BGN to END.\r\n\r\n[h5p id=\"33\"]\r\n\r\nDid you notice that the same keys are used to switch from END to BGN as BGN to END?\r\n\r\n<\/div>\r\n<\/div>\r\n&nbsp;\r\n<h1>Calculating the Rate Charged &amp; Down Payments on leases<\/h1>\r\nWhen leasing a car, it can be required to make a down payment. If a down payment is made, we deduct that from the selling price to determine the amount leased:\r\n<p style=\"text-align: center\">[latex] \\textrm{Amount Leased (PV)} = \\textrm{Selling Price} - \\textrm{Down Payment} [\/latex]<\/p>\r\nIf we instead need the selling price, we re-shuffle the above equation to give:\r\n<p style=\"text-align: center\">[latex] \\textrm{Selling Price} = \\textrm{Amount Leased (PV)} + \\textrm{Down Payment} [\/latex]<\/p>\r\n<p style=\"text-align: left\">Let us now look at Raj's lease. He is hoping to lease a Tesla Model X.<\/p>\r\n\r\n<h2>EXAMPLE 5.4.1<\/h2>\r\nRaj can lease a Tesla Model X car for three years. From the Tesla website, he finds the following pricing information:\r\n<ul>\r\n \t<li>Selling Price: $110,880<\/li>\r\n \t<li>Term: 36 months<\/li>\r\n \t<li>Required Down Payment: $7,500<\/li>\r\n \t<li>Monthly payment size: $1,702, the first monthly payment is due the day the car is purchased<\/li>\r\n \t<li>Amount owed (residual value) in 3 years to purchase the Model X: $50,568.84<\/li>\r\n<\/ul>\r\nWhat effective interest rate is Tesla charging on the 3-year lease?\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Check Your Knowledge 5.4.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nF<span style=\"text-align: initial;font-size: 14pt\">irst, calculate the amount leased (PV):<\/span>\r\n\r\n[h5p id=\"34\"]\r\n\r\n[h5p id=\"35\"]\r\n\r\nNext, enter the values into the BAII Plus:\r\n\r\n[h5p id=\"36\"]\r\n\r\n[h5p id=\"37\"]\r\n\r\nConclusion: Tesla is charging 3.75% effective on their 3-year lease.\r\n\r\n<\/div>\r\n<\/div>\r\n&nbsp;\r\n<h1>Cost of Financing for Leases<\/h1>\r\nWe also call the interest charged on leases the [pb_glossary id=\"1979\"]cost of financing[\/pb_glossary]. The same interest formula is used:\r\n<p style=\"text-align: center\">[latex] \\begin{align*} \\textrm{Cost of Financing} &amp;= \\textrm{Money Out} - \\textrm{Money In} = \\textrm{\\$ OUT} - \\textrm{\\$ IN} \\end{align*} [\/latex]<\/p>\r\nIn the case of car leases, we consider the selling price of the car, PV to be \u201cmoney in.\u201d We consider the regular payments (PMT) and the residual value (FV) to be \u2018money out\u2019:\r\n<table class=\"no-lines aligncenter\" style=\"border-collapse: collapse;width: 80%;height: 51px\" border=\"0\">\r\n<thead>\r\n<tr style=\"height: 18px\">\r\n<th style=\"width: 24%;height: 19px\">PV<\/th>\r\n<th style=\"width: 22%;height: 19px\">Interest<\/th>\r\n<th style=\"width: 26%;height: 19px\">PMT<\/th>\r\n<th style=\"width: 28%;height: 19px\">FV<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 24%;height: 16px\"><strong>Amount Leased<\/strong><\/td>\r\n<td style=\"width: 22%;height: 16px\"><strong>+\u00a0 %Charged<\/strong><\/td>\r\n<td style=\"width: 26%;height: 16px\"><span style=\"color: #ff0000\"><strong>=\u00a0 \u00a0Lease Payments<\/strong><\/span><\/td>\r\n<td style=\"width: 28%;height: 16px\"><span style=\"color: #ff0000\"><strong>+\u00a0 \u00a0Residual Value<\/strong><\/span><\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 24%;height: 16px\"><span style=\"font-size: 116%\">$ IN<\/span><\/td>\r\n<td style=\"width: 22%;height: 16px\"><span style=\"font-size: 116%\">$ IN<\/span><\/td>\r\n<td style=\"width: 26%;height: 16px\"><span style=\"color: #ff0000;font-size: 116%\">$ OUT<\/span><\/td>\r\n<td style=\"width: 28%;height: 16px\"><span style=\"color: #ff0000;font-size: 116%\">$ OUT<\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nThis gives us the following equation for cost of financing for leases:\r\n<p style=\"text-align: center\">[latex] \\begin{align*} \\textrm{Cost of Financing} &amp;= \\textrm{\\$ OUT} - \\textrm{\\$ IN}\\\\ &amp;=( \\textrm{Lease Payments}+ \\textrm{Residual Value}) - \\textrm{Amount Leased}\\\\ &amp;= ( \\textrm{PMT}\u00d7\\textrm{N}+\\textrm{FV})-\\textrm{PV} \\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 5.4.3<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n[h5p id=\"38\"]\r\n\r\n[h5p id=\"39\"]\r\n\r\n<\/div>\r\n<\/div>\r\n<h1>Key Takeaways<\/h1>\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Key Takeaways: Car Leases and Annuities Due<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n[h5p id=\"40\"]\r\n\r\n[h5p id=\"41\"]\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\"]","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 the rate and cost of financing for car leases and understand annuities due.<\/p>\n<\/div>\n<\/div>\n<p>Leasing a car (or vehicle) is much like renting a vehicle. The <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_2083_2128\">lessee<\/a> (person leasing the car) makes a series of equal-sized payments (<a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_2083_2129\">lease payments<\/a>), at regular intervals over the course of a fixed time period (<a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_2083_2130\">lease period<\/a>). These payments will be smaller than loan payments. This is because at the end of the lease, the lessee either must pay an additional amount called the <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_2083_2131\">residual value<\/a> to purchase the car or they must return the car to the car dealership. To calculate any of the above values, we enter the following in for each value:<\/p>\n<table class=\"no-lines aligncenter\" style=\"border-collapse: collapse;width: 80%;height: 51px\">\n<thead>\n<tr style=\"height: 18px\">\n<th style=\"width: 24%;height: 19px\">PV<\/th>\n<th style=\"width: 22%;height: 19px\">Interest<\/th>\n<th style=\"width: 26%;height: 19px\">PMT<\/th>\n<th style=\"width: 28%;height: 19px\">FV<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr style=\"height: 16px\">\n<td style=\"width: 24%;height: 16px\"><strong>Amount Leased<\/strong><\/td>\n<td style=\"width: 22%;height: 16px\"><strong>+\u00a0 %Charged<\/strong><\/td>\n<td style=\"width: 26%;height: 16px\"><span style=\"color: #ff0000\"><strong>=\u00a0 \u00a0Lease Payments<\/strong><\/span><\/td>\n<td style=\"width: 28%;height: 16px\"><span style=\"color: #ff0000\"><strong>+\u00a0 \u00a0Residual Value<\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 24%;height: 16px\"><strong><span style=\"font-size: 124%\">+<\/span><\/strong><\/td>\n<td style=\"width: 22%;height: 16px\"><strong><span style=\"font-size: 124%\">+<\/span><\/strong><\/td>\n<td style=\"width: 26%;height: 16px\"><strong><span style=\"color: #ff0000;font-size: 124%\">\u2212<\/span><\/strong><\/td>\n<td style=\"width: 28%;height: 16px\"><strong><span style=\"color: #ff0000;font-size: 124%\">\u2212<\/span><\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Leases are examples of <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_2083_985\">annuities due<\/a>. We will examine this term in the section below.<\/p>\n<p>See the sections below for key formulas, tips and examples related to leases and annuities due.<\/p>\n<h1>Ordinary Annuities vs Annuities Due<\/h1>\n<p>When calculating an <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_2083_892\">ordinary annuity<\/a> (an annuity where the payments occur at the end of each payment interval), you do not likely need to change anything in your calculator. By default, your calculator will be set to <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_2083_2089\">END<\/a> mode (which is the setting you need for ordinary annuities).<\/p>\n<p>It is also possible that payments occur at the beginning of each interval. In this case, you need to \u201ctell\u201d your calculator that the payments are occurring at the beginning of the payment interval. You do this by setting the calculator to <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_2083_2088\">BGN<\/a> mode. This type of annuity is called an annuity due.<\/p>\n<h1>How Do We SWITCH between Bgn and end on the BAII Plus?<\/h1>\n<h2>How Do We Set the BAII Plus to BGN?<\/h2>\n<ul>\n<li>Hit <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_2083_2104\">[2ND]<\/a> followed by <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_2083_2105\">[PMT]<\/a> on your calculator (this gets you into the BGN\/END menu).<\/li>\n<li>You will see END displayed on the screen. To change this to BGN, click on [<strong>2ND<\/strong>] and <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_2083_2106\">[ENTER]<\/a><\/li>\n<li>You will now see BGN displayed on the screen as well as in the top right of the screen.<\/li>\n<li>Hit [<strong>2ND<\/strong>] followed by <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_2083_2117\">[CPT]<\/a> to exit the BGN\/END menu.<\/li>\n<li><strong>Be careful!<\/strong>\u00a0 Ordinary annuities are more common that annuities due so once you have completed your annuity due question, turn off BGN (ie: set your calculator back to END).<\/li>\n<\/ul>\n<h2>How Do We Set the BAII Plus to END?<\/h2>\n<ul>\n<li>Hit [<strong>2ND<\/strong>] followed by [<strong>PMT<\/strong>] on your calculator.<\/li>\n<li>You will see BGN displayed on the screen. To change this to END, click on [<strong>2ND<\/strong>] and [<strong>ENTER<\/strong>].<\/li>\n<li>You will now see END displayed on the screen and you will see BGN disappear from the top right of the calculator screen.<\/li>\n<li>Hit [<strong>2ND<\/strong>] followed by [<strong>CPT<\/strong>] to exit the BGN\/END menu.<\/li>\n<\/ul>\n<p>Now, you can practice these steps in the exercise below.<\/p>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Check Your Knowledge 5.4.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Drag the keys onto the calculator screen in the correct order to switch from END to BGN.<\/p>\n<div id=\"h5p-33\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-33\" class=\"h5p-iframe\" data-content-id=\"33\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"5.4.1 Switch Between BGN and END\"><\/iframe><\/div>\n<\/div>\n<p>Drag the keys onto the calculator screen in the correct order to switch from BGN to END.<\/p>\n<div id=\"h5p-33\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-33\" class=\"h5p-iframe\" data-content-id=\"33\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"5.4.1 Switch Between BGN and END\"><\/iframe><\/div>\n<\/div>\n<p>Did you notice that the same keys are used to switch from END to BGN as BGN to END?<\/p>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<h1>Calculating the Rate Charged &amp; Down Payments on leases<\/h1>\n<p>When leasing a car, it can be required to make a down payment. If a down payment is made, we deduct that from the selling price to determine the amount leased:<\/p>\n<p style=\"text-align: center\">[latex]\\textrm{Amount Leased (PV)} = \\textrm{Selling Price} - \\textrm{Down Payment}[\/latex]<\/p>\n<p>If we instead need the selling price, we re-shuffle the above equation to give:<\/p>\n<p style=\"text-align: center\">[latex]\\textrm{Selling Price} = \\textrm{Amount Leased (PV)} + \\textrm{Down Payment}[\/latex]<\/p>\n<p style=\"text-align: left\">Let us now look at Raj&#8217;s lease. He is hoping to lease a Tesla Model X.<\/p>\n<h2>EXAMPLE 5.4.1<\/h2>\n<p>Raj can lease a Tesla Model X car for three years. From the Tesla website, he finds the following pricing information:<\/p>\n<ul>\n<li>Selling Price: $110,880<\/li>\n<li>Term: 36 months<\/li>\n<li>Required Down Payment: $7,500<\/li>\n<li>Monthly payment size: $1,702, the first monthly payment is due the day the car is purchased<\/li>\n<li>Amount owed (residual value) in 3 years to purchase the Model X: $50,568.84<\/li>\n<\/ul>\n<p>What effective interest rate is Tesla charging on the 3-year lease?<\/p>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Check Your Knowledge 5.4.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>F<span style=\"text-align: initial;font-size: 14pt\">irst, calculate the amount leased (PV):<\/span><\/p>\n<div id=\"h5p-34\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-34\" class=\"h5p-iframe\" data-content-id=\"34\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"5.4.2.1 Car Lease Example - Amount Leased Calculation\"><\/iframe><\/div>\n<\/div>\n<div id=\"h5p-35\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-35\" class=\"h5p-iframe\" data-content-id=\"35\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"5.4.2.1 Car Lease Example - Amount Leased Calculation Answer\"><\/iframe><\/div>\n<\/div>\n<p>Next, enter the values into the BAII Plus:<\/p>\n<div id=\"h5p-36\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-36\" class=\"h5p-iframe\" data-content-id=\"36\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"5.4.2.2 Calculating the interest rate on a car lease\"><\/iframe><\/div>\n<\/div>\n<div id=\"h5p-37\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-37\" class=\"h5p-iframe\" data-content-id=\"37\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"5.4.2.2 Car Lease Calculator Keys Answer\"><\/iframe><\/div>\n<\/div>\n<p>Conclusion: Tesla is charging 3.75% effective on their 3-year lease.<\/p>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<h1>Cost of Financing for Leases<\/h1>\n<p>We also call the interest charged on leases the <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_2083_1979\">cost of financing<\/a>. The same interest formula is used:<\/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>In the case of car leases, we consider the selling price of the car, PV to be \u201cmoney in.\u201d We consider the regular payments (PMT) and the residual value (FV) to be \u2018money out\u2019:<\/p>\n<table class=\"no-lines aligncenter\" style=\"border-collapse: collapse;width: 80%;height: 51px\">\n<thead>\n<tr style=\"height: 18px\">\n<th style=\"width: 24%;height: 19px\">PV<\/th>\n<th style=\"width: 22%;height: 19px\">Interest<\/th>\n<th style=\"width: 26%;height: 19px\">PMT<\/th>\n<th style=\"width: 28%;height: 19px\">FV<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr style=\"height: 16px\">\n<td style=\"width: 24%;height: 16px\"><strong>Amount Leased<\/strong><\/td>\n<td style=\"width: 22%;height: 16px\"><strong>+\u00a0 %Charged<\/strong><\/td>\n<td style=\"width: 26%;height: 16px\"><span style=\"color: #ff0000\"><strong>=\u00a0 \u00a0Lease Payments<\/strong><\/span><\/td>\n<td style=\"width: 28%;height: 16px\"><span style=\"color: #ff0000\"><strong>+\u00a0 \u00a0Residual Value<\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 24%;height: 16px\"><span style=\"font-size: 116%\">$ IN<\/span><\/td>\n<td style=\"width: 22%;height: 16px\"><span style=\"font-size: 116%\">$ IN<\/span><\/td>\n<td style=\"width: 26%;height: 16px\"><span style=\"color: #ff0000;font-size: 116%\">$ OUT<\/span><\/td>\n<td style=\"width: 28%;height: 16px\"><span style=\"color: #ff0000;font-size: 116%\">$ OUT<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>This gives us the following equation for cost of financing for leases:<\/p>\n<p style=\"text-align: center\">[latex]\\begin{align*} \\textrm{Cost of Financing} &= \\textrm{\\$ OUT} - \\textrm{\\$ IN}\\\\ &=( \\textrm{Lease Payments}+ \\textrm{Residual Value}) - \\textrm{Amount Leased}\\\\ &= ( \\textrm{PMT}\u00d7\\textrm{N}+\\textrm{FV})-\\textrm{PV} \\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 5.4.3<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"h5p-38\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-38\" class=\"h5p-iframe\" data-content-id=\"38\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"5.4.3 Calculating the Cost of Financing\"><\/iframe><\/div>\n<\/div>\n<div id=\"h5p-39\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-39\" class=\"h5p-iframe\" data-content-id=\"39\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"5.4.3 Calculating the Cost of Financing Answer\"><\/iframe><\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Key Takeaways<\/h1>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Key Takeaways: Car Leases and Annuities Due<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"h5p-40\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-40\" class=\"h5p-iframe\" data-content-id=\"40\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"5.4 Key Takeaways for Leases and Annuities Due\"><\/iframe><\/div>\n<\/div>\n<div id=\"h5p-41\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-41\" class=\"h5p-iframe\" data-content-id=\"41\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"5.4 Key Takeaways for Leases and Annuities Due Answers\"><\/iframe><\/div>\n<\/div>\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<div class=\"glossary\"><span class=\"screen-reader-text\" id=\"definition\">definition<\/span><template id=\"term_2083_2128\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_2083_2128\"><div tabindex=\"-1\"><p>Person or company holding the lease. Example: person who is leasing a car.<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_2083_2129\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_2083_2129\"><div tabindex=\"-1\"><p>Equal sized payments for a lease.<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_2083_2130\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_2083_2130\"><div tabindex=\"-1\"><p>Duration of a lease (fixed time period).<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_2083_2131\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_2083_2131\"><div tabindex=\"-1\"><p>Size of final lease payment required. Example: final payment required to own a car at the end of the car lease.<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_2083_985\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_2083_985\"><div tabindex=\"-1\"><p>An annuity with deposits or payments at the beginning of the payment period.<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_2083_892\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_2083_892\"><div tabindex=\"-1\"><p>An annuity where the payments occur at the end of each 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_2083_2089\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_2083_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_2083_2088\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_2083_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><template id=\"term_2083_2104\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_2083_2104\"><div tabindex=\"-1\"><p>The [2ND] function key (near the top left on the BAII Plus) allows the user to access the secondary menus. Example: [2ND][PMT] accesses the BGN menu.<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_2083_2105\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_2083_2105\"><div tabindex=\"-1\"><p>The 'payment' key within the TVM (time value of money keys) in the BAII Plus Calculator.<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_2083_2106\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_2083_2106\"><div tabindex=\"-1\"><p>The [ENTER] key (top left on the BAII Plus) is used to set values within the calculator's menus.<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_2083_2117\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_2083_2117\"><div tabindex=\"-1\"><p>Compute key on BAII Plus. Computes selected value.<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_2083_1979\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_2083_1979\"><div tabindex=\"-1\"><p>The amount of interest we must repay on the loan.<\/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":865,"menu_order":4,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-2083","chapter","type-chapter","status-publish","hentry"],"part":46,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/pressbooks\/v2\/chapters\/2083","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\/865"}],"version-history":[{"count":26,"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/pressbooks\/v2\/chapters\/2083\/revisions"}],"predecessor-version":[{"id":3844,"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/pressbooks\/v2\/chapters\/2083\/revisions\/3844"}],"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\/2083\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/wp\/v2\/media?parent=2083"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/pressbooks\/v2\/chapter-type?post=2083"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/wp\/v2\/contributor?post=2083"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/wp\/v2\/license?post=2083"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}