What is the monthly payment size of a 21-year mortgage for $169 600 and an interest rate of 7.2% compounded semi-annually?

Question

Quizplus · Accepted Answer

Step 1: Convert the annual interest rate to a semi-annual rate by dividing by 2.
7.2% / 2 = 3.6%

Step 2: Calculate the number of payments by multiplying the number of years by 2 (since there are two semi-annual periods in one year).
21 years × 2 = 42 payments

Step 3: Use the formula for mortgage payments:
Payment = (P × r) ÷ (1 − (1 + r)-n)

where:
P = principal amount (the amount borrowed) = $169,600
r = interest rate per period = 3.6% (since we divided by 2)
n = total number of payments = 42

Payment = ($169,600 × 0.036) ÷ (1 − (1 + 0.036)-42)
Payment = $9,062.56 ÷ 17.967
Payment = $504.19 (rounded to the nearest cent)

Step 4: Double-check the payment by multiplying by the number of payments per year (2) and comparing to the annual interest rate.
$504.19 × 2 = $1008.38
$1008.38 ÷ $169,600 = 0.00596 (rounded to five decimal places)
0.00596 × 2 = 0.01192 (the annual rate equivalent)
0.01192 × 100 = 1.192% (the annual rate percentage)
This is close to the original rate of 7.2%, which confirms that the payment calculation is reasonable.

Therefore, the monthly payment size is $1008.38 ÷ 12 = $84.03. Rounded to the nearest cent it is $84.04.
The closest answer option is B) $1296.11, which is not correct.
Therefore, there is no best choice.

What Is the Monthly Payment Size of a 21-Year Mortgage