Question

The balance on a mortgage was $47,500 and an interest rate of 3.50% compounded semi-annually was charged for the remaining 3-year term. Monthly payments were made to settle the mortgage.

a. Calculate the size of the monthly payments.

Round up to the next whole number

b. If the monthly payments were set at $1,542, how long would it take to pay off the mortgage?

years

months

Express the answer in years and months, rounded to the next payment period

c. If the monthly payments were set at $1,542, calculate the size of the final payment.

Answer 1

a) $1392

b) 2 years, 8 months

c) $1474.10

Explanation:

You want the monthly payments on a 3-year $47,500 loan at 3.5% compounded semi-annually. When the payments are $1542, you want the payoff time and the amount of the final payment.

Compounding

Usually interest is compounded at the same frequency as the payments. When payments are paid monthly and compounding is semi-annual, the calculation can be a bit tricky. Here, we let a calculator figure it out. We expect the calculation is accomplished by translating the effective annual interest rate to an effective monthly rate. That monthly rate will be ...

(1 +0.035/2)^(1/6) -1 = 0.289562% per month, an APR of about 3.4747%

a) Monthly payments

The calculator tells us the monthly payments will be $1392.

b) Payoff time

With monthly payments of $1542, the calculator tells us the payoff time will be 32 months, about 2 years, 8 months.

c) Final payment

Paying 1542 for 32 months will result in an overpayment of $67.90, so the final payment will be less by this amount.

The final payment is $1474.10.

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