for a fixed loan amount, what happens to the monthly payment as the annual rate increases? a. as the annual…

for a fixed loan amount, what happens to the monthly payment as the annual rate increases? a. as the annual rate increases, the monthly payment increases b. as the annual rate increases, the monthly payment decreases c. as the annual rate increases, the monthly payment stays the same d. no correlation

for a fixed loan amount, what happens to the monthly payment as the annual rate increases? a. as the annual rate increases, the monthly payment increases b. as the annual rate increases, the monthly payment decreases c. as the annual rate increases, the monthly payment stays the same d. no correlation

Answer

Explanation:

Step1: Recall loan - payment formula concept

The formula for the monthly payment $M$ of a fixed - rate loan is $M = P\frac{r(1 + r)^n}{(1 + r)^n-1}$, where $P$ is the principal loan amount, $r$ is the monthly interest rate, and $n$ is the total number of payments. If the annual interest rate $R$ increases, the monthly interest rate $r=\frac{R}{12}$ also increases.

Step2: Analyze the effect on the formula

As $r$ increases in the formula $M = P\frac{r(1 + r)^n}{(1 + r)^n-1}$, with $P$ (loan amount) fixed, the numerator $P\times r(1 + r)^n$ increases at a faster rate than the denominator $(1 + r)^n-1$. So, the value of $M$ (monthly payment) increases.

Answer:

a. as the annual rate increases, the monthly payment increases