A 20-year mortgage with monthly payments has a principal outstanding of $125,000. Interest is at 8% compounded semi-annually. What are the monthly payments?

Question

Quizplus · Accepted Answer

First, we need to calculate the semi-annual interest rate:
r = 8% / 2 = 4%

Next, we need to calculate the number of semi-annual periods over 20 years:
n = 20 years * 2 = 40 semi-annual periods

Using the formula for the present value of an annuity, we can calculate the monthly payments:

PMT = (r * PV) / (1 - (1 + r)^(-n))
where PMT is the monthly payment, PV is the principal outstanding, r is the semi-annual interest rate, and n is the number of semi-annual periods.

Substituting the given values, we get:
PMT = (0.04 * 125000) / (1 - (1 + 0.04)^(-40))
PMT = $1,035.45

Therefore, the best choice is B.

A 20-Year Mortgage with Monthly Payments Has a Principal Outstanding