Question

Obtain the principle amount repaid during the last ten years of a $425,000 mortgage when N=20 and k=8.5%, assuming monthly compounding. (SHOW WORKING FOR EACH STEP) Also please explain how P1 is equal to 121.

Answer 1

Original Mortgage Amount = $ 425000, Mortgage Tenure = N = 20 years or (12 x 20) = 240 months, Interest Rate = 8.5 % per annum

Monthly Interest Rate = (8.5 / 12) = 0.7083 %

Let the monthly mortgage repayments be $ P

Therefore, 425000 = P x (1/0.007083) x [1-{1/(1.007083)^(240)}]

425000 = P x 115.234

P = 425000 / 115.234 = $ 3688.15

Assuming that the entire original mortgage amount is completely repaid during the 20 year mortgage tenure, the amount of principal repaid in the last ten years should equal the portion of the original mortgage outstanding as of the end of Year 10.

Principal Outstanding at the end of Year 10 = Principal Repaid in the last 10 years = Present Value of Remaining Monthly Mortgage Repayments at the end of Year 10 = 3688.15 x (1/0.007083) x [1-{1/(1.007083)^(120)}] = $ 297470.72