Calculate the size of the monthly mortgage loan payment if a $121,500 loan at 7% compounded semi-annually is to be paid off over 18 years.

Question

Quizplus · Accepted Answer

The correct calculation involves using the formula for a fixed-rate mortgage, which is often represented as $M = P\frac{r(1+r)^n}{(1+r)^n-1}$, where $M$ is the monthly payment, $P$ is the principal amount (in this case, $121,500), $r$ is the monthly interest rate (annual rate divided by 12), and $n$ is the total number of payments (months). Given an annual interest rate of 7% compounded semi-annually, we first need to adjust this to a monthly rate. However, the compounding frequency doesn't directly affect the calculation since we're looking for a monthly payment and thus use the nominal monthly interest rate, which is $7\% / 12 = 0.005833$. Over 18 years (or 216 months), the formula gives us the monthly payment. Plugging the values into the formula or using a financial calculator with these inputs will give us the closest value to $983.75, making option A the correct choice.

Calculate the Size of the Monthly Mortgage Loan Payment If