How much total principal is repaid between the 1st and 7th payment interval of a 4.5-year loan for $4887 at an interest rate of 7.4% compounded monthly and the payments are also monthly. Round your answer to the nearest dollar.

Question

Quizplus · Accepted Answer

To solve this, we first need to find the monthly payment amount using the loan formula for payments on an amortizing loan, which is $PMT = P \times \frac{r(1+r)^n}{(1+r)^n-1}$, where $P$ is the principal amount ($4887), $r$ is the monthly interest rate (7.4% annual rate divided by 12 months = 0.0071667), and $n$ is the total number of payments (4.5 years times 12 months/year = 54 payments). Plugging in the values, we get the monthly payment amount. Then, we calculate the total interest paid between the 1st and 7th payment and subtract that from the total payments made in that period to find the principal repaid. The correct answer is found by accurately calculating these values and rounding to the nearest dollar, which results in $546.

How Much Total Principal Is Repaid Between the 1st and 7th