Question

John recently bought a house, and he financed it with a $250,000, 30-year

mortgage with an annual interest rate of 7 percent. The mortgage payments are

made at the end of each year. What total dollar amount of the mortgage

payments during the first three years will go towards paying interest?

Answer 1

Mortgage = $ 250000, Mortgage Tenure = 30 years, Payment Frequency: Annual, Annual Interest Rate = 7%
Let the annual mortgage repayments be $ N

Therefore, 250000 = N x (1/0.07) x [1-{1/(1.07)^(30)}]

250000 = N x 12.409

N = 250000 / 12.409 = $ 20146.6

Mortgage Outstanding after Year 3 = Sum of the Present Values of the Remaining Mortgage Payments = 20146.6 x (1/0.07) x [1-{1/(1.07)^(27)}] = $ 241491.44

Principal Repaid in the first 3 years = 250000 - 241491.44 = $ 8508.56

Interest Paid = Annual Mortgage Payments x 3 - Principal Repaid = 3 x 20146.6 - 8508.56 = $ 51931.24