Calculate the Interest on a Mortgage

Question

33.Suppose you have just obtained a 30-year home mortgage in the amount of $292,000 at an APR of 5.75%. By finding the required monthly payment and also the monthly payment that you would need to make in order to pay off the loan in 20 years, determine the amount you would save in interest charges by paying off the loan in 20 years. (a) $83,052.00 (b) $120,392.40 (c) $121,431.60 (d) $124,578.00 34.

Answer 1

For this one we will need the mortgage monthly payment formula

Monthly Payment = P [ i (1 + i) ^ n] / [ (1 + i)^n - 1]

P = Principal

i = Monthly Interest

n = Number of months to repay loan

First, calculate the number of month to repay loan

30 year x 12 months = 360 months

20 year x 12 months = 240 months

Next, we will calculate the monthly interest rate

5.75% / 12 months = 0.48%

Next we'll calculate the monthly payments for each period (note: some rounding below)

30 years

292,000 [0.0048 (1.0048)^360] / [1.0048^360 - 1]

292,000 [0.0269] / [4.606]

292,000 x .0058

1,704.03 monthly payment

20 years

292,000 [0.0048 (1.0048)^240] / [1.0048^240 - 1]

292,000 [0.0151] / [3.156]

292,000 x .0070

2,050.08 monthly payment

Now that we have the monthly payments, we can calculate the interest saved. Take the monthly payments for each and figure out how much would be spent in payments during the period. Anything in excess of the principal will be considered interest payments.

30 years - 1,704.03 * 12 * 30 = 613,450.80 total payments

20 years - 2,050.08 * 12 * 20 = 492,019.20 total payments

613,450.80 - 292,000 = 321,450.80 interest paid

492,019.20 - 292,000 = 200,019.20 interest paid

Finally, the difference in interest paid will get us the answer.

321,450.80 - 200,019.20 = 121,431.60 (C)

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