Peter recently purchased a new home with a25-year mortgage loan of $250,000 at 8% compounded monthly, What is the total amount of interest Peter will pay the bank over the life of the loan?
A)$528,860
B)$328,860
C)$335,500
D)$250,000

Question

Peter recently purchased a new home with a25-year mortgage loan of $250,000 at 8% compounded monthly, What is the total amount of interest Peter will pay the bank over the life of the loan?
A)​$528,860
B)​$328,860
C)​$335,500
D)​$250,000

Quizplus · Accepted Answer

To find the total amount of interest paid over the life of the loan, first, calculate the monthly payment using the formula for a fixed-rate mortgage, which is $PMT = P \frac{r(1+r)^n}{(1+r)^n - 1}$, where $P$ is the principal amount ($250,000), $r$ is the monthly interest rate (annual rate divided by 12, so 0.08/12), and $n$ is the total number of payments (25 years * 12 months = 300 payments). Plugging in the numbers: $PMT = 250,000 \frac{(0.08/12)(1+0.08/12)^{300}}{(1+0.08/12)^{300} - 1}$. This calculation gives us the monthly payment amount. Then, multiply the monthly payment by the total number of payments (300) to get the total amount paid over the life of the loan. Subtract the principal ($250,000) from this total to find the total interest paid.The calculation for the monthly payment gives approximately $1,930.48. Multiplying this by 300 gives $579,144. Subtracting the principal ($250,000) from this total gives $329,144 in interest, which is closest to option B, $328,860, acknowledging a slight approximation in the final step or rounding differences.

Peter Recently Purchased a New Home with A25-Year Mortgage Loan