{"id":887,"date":"2020-08-10T11:27:44","date_gmt":"2020-08-10T15:27:44","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/?post_type=chapter&p=887"},"modified":"2021-07-12T16:29:17","modified_gmt":"2021-07-12T20:29:17","slug":"mortgages","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/chapter\/mortgages\/","title":{"raw":"5.10 Mortgages","rendered":"5.10 Mortgages"},"content":{"raw":"
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Learning Outcomes<\/p>\r\n\r\n<\/header>\r\n

\r\n\r\nCalculate the payment size, balance, principal repaid or interest charged during a mortgage and understand how to renew a mortgage.\r\n\r\n<\/div>\r\n<\/div>\r\n\"\"It is often necessary to take out a mortgage when purchasing a home or property.\u00a0 A mortgage is usually a long-term (roughly 25 year), [pb_glossary id=\"891\"]general[\/pb_glossary] (P\/Y \u2260 C\/Y), [pb_glossary id=\"892\"]ordinary[\/pb_glossary] annuity (PMTs at END of interval).\u00a0 Buyers can choose a [pb_glossary id=\"895\"]fixed[\/pb_glossary] or [pb_glossary id=\"897\"]variable rate[\/pb_glossary] mortgage.\u00a0 A fixed rate mortgage means that the interest rate charged remains fixed for the [pb_glossary id=\"896\"]mortgage term[\/pb_glossary].\u00a0 A variable rate mortgage means that the interest rate varies throughout the mortgage term. In general, the buyer (mortgage holder) is required to pay down some of the balance owing ([pb_glossary id=\"898\"]principal[\/pb_glossary]) on the mortgage in addition to the interest charges each interval.\r\n

History of How Mortgages Evolved over the Years<\/h1>\r\nIn the 1900\u2019s, home buyers who took out a mortgage only paid the interest owed each month.\u00a0 The buyer would save up while making these interest-only payments and fully repay the mortgage when they had enough saved.[footnote]Information thanks to the Financial Services Commission of Ontario: https:\/\/www.fsco.gov.on.ca\/en\/mortgage\/Pages\/history.aspx<\/a>[\/footnote]\r\n\r\nMajor world events (like the first world war & great depression) changed this practice.\u00a0 Large numbers of people were unable to pay their mortgages.\u00a0 Because of this, buyers were then required to pay some of the balance owing ([pb_glossary id=\"898\"]principal[\/pb_glossary]) each payment interval in addition to the interest owed each month.\u00a0 To further protect lenders, in 1946, the \u201cCanada Mortgage and Housing Corporation(CMHC)\u201d was created.\u00a0 The CMHC insures buyers\u2019 mortgages if the buyer puts down less than a minimum % down payment.[footnote]Currently, the CMHC insures mortgages with \u201cmortgage default insurance\u201d if the less than a 20% down payment is made at the start of the mortgage.[\/footnote]\u00a0 This protects lenders if a buyer [pb_glossary id=\"899\"]defaults[\/pb_glossary] on their mortgage (can\u2019t pay their mortgage).\r\n\r\nBefore the 1970\/80\u2019s, buyers would be guaranteed a [pb_glossary id=\"900\"]fixed interest rate[\/pb_glossary] for the entire duration of their mortgage.\u00a0 This changed after the interest rate inflation in the 1970\u2019s and 80\u2019s (interest rates hit a record high of 21.46%).\u00a0 Banks who had previously locked in interest rates with buyers were missing out on thousands of potential dollars in interest when buyer were locked in at rates as low as 6.9% and when the current interest rate was 21.46%.\u00a0 After the interest rate inflation of the 1970\u2019s and 1980\u2019s, banks created \u201c[pb_glossary id=\"901\"]mortgage terms[\/pb_glossary].\u201d\r\n

Mortgage Terms<\/h1>\r\nA mortgage term is the length of time your mortgage agreement and interest rate will be in effect.[footnote]Information thanks to https:\/\/www.canada.ca\/en\/financial-consumer-agency\/services\/financial-toolkit\/mortgages\/mortgages-2\/6.html<\/a>[\/footnote]\u00a0 Mortgage terms are, most often, 5 years in length but can vary anywhere from 6 months to 10 years in length.\u00a0 If the buyer chooses a fixed-rate mortgage, they are guaranteed a fixed interest rate for the duration of the mortgage term.\u00a0 After the term is \u2018up\u2019 (after the time period defined by the term has passed), the buyer negotiates a new interest rate with the lender (bank).\u00a0 The buyer [pb_glossary id=\"904\"]renews[\/pb_glossary] their mortgage.\r\n\r\nBasically, a new mortgage is drawn up at the end of each term when the buyer renews their mortgage.\u00a0 The buyer can pay off part (or all) of the balance owing with a lump-sum payment.\u00a0 The buyer can move their mortgage to another bank. The buyer is charged interest at the new interest rate and pays this interest on the current balance (principal) owing on the mortgage.\r\n\r\nIf each term is 5 years in length, a buyer will renew their mortgage roughly five times on a 25-year mortgage.\u00a0 The full length of the mortgage (ex: 25 years) is the [pb_glossary id=\"905\"]amortization period.[\/pb_glossary]\r\n

Constructing Amortization Tables<\/h1>\r\n[pb_glossary id=\"3505\"]Amortization[\/pb_glossary] is \"the process of paying off debt over time with regular installments of interest and principal sufficient to repay the loan in full by its [pb_glossary id=\"3289\"]maturity date.[\/pb_glossary][footnote]https:\/\/www.investopedia.com\/terms\/a\/amortization.asp<\/a>[\/footnote]\"\r\n\r\nWe can create an [pb_glossary id=\"920\"]amortization table[\/pb_glossary] (or schedule) to show the amount of principal and interest that make up each payment. The table also shows the balance owing after each payment. The table can run until the loan (or mortgage) if fully paid off or to the end of the term.\r\n\r\nLet us now look at an example of an amortization schedule for Kerry \u2014 she just bought a car and borrowed some money from her line of credit to do so.\r\n

Example 5.10.1<\/h2>\r\nKerry purchases a new Toyota Rav4. She borrows $16,000 from her line of credit for the purchase. She is charged 3% compounded monthly on the line of credit. Kerry wants to repay her line of credit with 6 monthly payments. The first payment will be in one month. Construct an amortization schedule and use it to answer how much interest she will pay in total and what the size of her final payment will be. Assume Kerry owed nothing on her line of credit before she borrowed the $16,000.\r\n\r\nIn order to construct the amortization schedule, we need to determine the size of Kerry's monthly payments:\r\n\r\n\r\n\r\n\r\n\r\n
B\/E<\/th>\r\nP\/Y<\/th>\r\nC\/Y<\/th>\r\nN<\/th>\r\nI\/Y<\/th>\r\nPV<\/th>\r\nPMT<\/th>\r\nFV<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
END<\/td>\r\n12<\/td>\r\n12<\/td>\r\n6<\/td>\r\n3<\/td>\r\n+16,000<\/td>\r\nCPT<\/strong>\u00a0\u22122,690.05<\/span><\/td>\r\n0<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nLet's round Kerry's payment up to the next dollar[footnote]For mortgages and loans, banks round mortgage payments up to the next dollar or the next cent. The final mortgage (or loan) payment is smaller as a result of the regular overpayments.[\/footnote] which means that Kerry will pay $2,691 per month.\r\n\r\nBecause we round up Kerry's payments, this means that she will overpay by roughly $0.95 per month. This makes her final payment slightly smaller. <\/span>Let us now construct the amortization schedule to determine the size of this final payment as well as the interest paid and balance outstanding each month.\r\n

Line of Credit Amortization Table<\/h3>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Payment #<\/strong><\/td>\r\nPayment (PMT)<\/strong><\/td>\r\nInterest Paid (INT)<\/strong><\/td>\r\nPrincipal Repaid (PRN)<\/strong><\/td>\r\nEnding Balance (BAL)<\/strong><\/td>\r\n<\/tr>\r\n<\/thead>\r\n
1<\/td>\r\n$2,691<\/td>\r\n$16,000\u00d70.0025 =$40<\/td>\r\n$2,691\u2212$40 =$2,651<\/td>\r\n$16,000\u2212$2,651 = $13,349<\/td>\r\n<\/tr>\r\n
2<\/td>\r\n$2,691<\/td>\r\n$13,349\u00d70.0025 =$33.37<\/td>\r\n$2,691\u2212$33.37 =$2,657.63<\/td>\r\n$13,349\u2212$2,657.63 = $10,691.37<\/td>\r\n<\/tr>\r\n
3<\/td>\r\n$2,691<\/td>\r\n$10,691.37\u00d70.0025 =$26.73<\/td>\r\n$2,691\u2212$26.73 =$2,664.27<\/td>\r\n$10,691.37\u2212$2,664.27 =$8,027.10<\/td>\r\n<\/tr>\r\n
4<\/td>\r\n$2,691<\/td>\r\n$8,027.10\u00d70.0025 =$20.07<\/td>\r\n$2,691\u2212$20.07 =$2,670.93<\/td>\r\n$8,027.10\u2212$2,670.93 =$5,356.17<\/td>\r\n<\/tr>\r\n
5<\/td>\r\n$2,691<\/td>\r\n$5,356.17\u00d70.0025 = $13.39<\/td>\r\n$2,691\u2212$13.39 =$2,677.61<\/td>\r\n$5,356.17\u2212$2,677.61 =$2,678.56<\/td>\r\n<\/tr>\r\n
6<\/td>\r\n$2,691[footnote]This will not be the actual size of the final payment. The final payment will actually be equal to this value minus the overpayment (final ending balance) =$2,691\u2212$5.74 = $2,685.25 [\/footnote]<\/td>\r\n$2,678.56\u00d70.0025 =$6.70<\/td>\r\n$2,691\u2212$6.70 =$2,684.30<\/td>\r\n$2,678.56\u2212$2,684.30 =\u2212$5.74<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

Key Takeaways for the Above Amortization Table<\/h3>\r\n