Question

6. (3 points) Consider a 15-year $170,000 mortgage with an interest rate of 5.75 % , and with monthly payments: 0 If the borrower wants to pay off the remaining balance on the mortgage after making the 99th payment, what is the remaining balance on the mortgage? e How much cumulative interest has been paid? How much cumulative principal has been paid?

Answer 1

Amount of mortgage $170,000 Interest rate 5.75% * 1/12 = 0.47916667% Per month Term 15 Years* 12 = 180 Months Monthly payment = Amount of mortgage I/[1 - (1+I^-n] = $170,000 0.47916667% / [1 - (1 +0.47916667% )^-180] = $814.5833333/0.57702414 = S1,411.697148 = S1,411.7 (Rounded) Remaining balance of loan after 99th payment = Amount of mortgage* (1+IYn - Monthly payment* [ 1 +I'n - 1]/I = S170,000 (1 +0.47916667% )^99 - $1,411.7 * [(1 +0.47916667%^99 - 1]/ 0.47916667% = $170,000* 1.605189943 - $1,411.7* 126.3005098 = $272,882.2903 - $178,298.4297 = $94,583.86056 Ans a) Remaining balance of mortgage = $94,583.86 (Rounded) b) Cumulative principal has been paid = Amount of mortgage - Remaining balance = S170,000 S94,583.86 = $75,416.14 c) Cumulative interest has been paid = Total amount paid - Principal amount paid = S1,411.7 Per month * 99 Months - $75,416.14 = S64,342.16