for a fixed loan amount, what happens to the ...
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