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Please help to answer part C only. Answer is $49,331.78
Ten years ago, you entered into an 25-year, fixed-rate mortgage at 6 % annual interest rate with monthly payments of $1,198.4
(b) Today, you would like to make an immediate $50,000 lump sum payment to shorten the payment duration. When will you pay of
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Answer #1

Original Tenure = 25 years, Remaining Tenure = 25 - 10 = 15 years, Fixed Rate = 6%, Monthly Repayments = $ 1198.4

Applicable Monthly Rate = 6/12 = 0.5 %

Outstanding Mortgage at the end of Year 10 = 1198.4 x (1/0.005) x [1-{1/(1.005)^(180)}] = $ 142014.612

Lump sum Payment = $ 50000

Remaining Mortgage = 142014.612 - 50000 = $ 92014.612

Let the number of additional required payments be N

Therefore, 92014.612 = 1198.4 x (1/0.005) x [1-{1/(1.005)^(N)}]

0.3839061 = [1-{1/(1.005)^(N)}]

1/(1.005)^(N) = 0.616094

(1.005)^(N) = 1.62313

N = log1.0051.62313 = 97.113 months ~ 98 months

Total Payment Made = 98 x 1198.4 + 120 x 1198.4 = 260188.4016

Total Payment under Original Repayment Plan = 300 x 1198.4 = $ 359520

Interest Saved = 359520 - 260188.4016 = $ 99331.78

NOTE: Please check the answer provided by you as I have checked the calculation multiple times and the answer for portion (b) is indeed $ 99331.78

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