Solve the problem. If necessary, refer to the table below.
-In order to purchase a home, a family borrows $150,000 at an annual interest rate of 7.7% to be paid back over a 15-year period in equal monthly payments. What is their monthly payment? Round
The answer to the nearest cent.

Question

Solve the problem. If necessary, refer to the table below. 
-In order to purchase a home, a family borrows $150,000 at an annual interest rate of 7.7% to be paid back over a 15-year period in equal monthly payments. What is their monthly payment? Round
The answer to the nearest cent.

Quizplus · Accepted Answer

The monthly payment for a fixed-rate mortgage can be calculated using the formula for the monthly payment of an annuity: $PMT = P \times \frac{r(1 + r)^n}{(1 + r)^n - 1}$, where $P$ is the principal amount borrowed, $r$ is the monthly interest rate (annual rate divided by 12), and $n$ is the total number of payments (years times 12). For this problem, $P = $150,000$, the annual interest rate is 7.7%, so the monthly interest rate $r = 7.7\% / 12 = 0.0077 / 12$, and $n = 15 \times 12 = 180$. Plugging these values into the formula gives the monthly payment, which rounds to $1407.62.

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