Question

alexa is buying a car and needs to take out a loan for $23,000. the bank is offering an annual interest rate of 6.3%, compounded monthly, for a 5 - year loan. using the formula below, determine her monthly payment, to the nearest dollar.

$m = \frac{pr(1 + r)^n}{(1 + r)^n - 1}$

$m=$ the monthly payment
$p=$ the amount borrowed
$r=$ the interest rate per month
$n=$ the number of payments

Explanation:

Step1: Calculate monthly interest rate

$r=\frac{6.3\%}{12}= 0.00525$

Step2: Calculate number of payments

$n = 5\times12=60$

Step3: Identify principal amount

$P = 23000$

Step4: Substitute values into formula

$M=\frac{23000\times0.00525\times(1 + 0.00525)^{60}}{(1 + 0.00525)^{60}-1}$
First, calculate $(1 + 0.00525)^{60}\approx1.37537$.
Then, $23000\times0.00525 = 120.75$.
$120.75\times1.37537\approx166.08$.
$1.37537-1 = 0.37537$.
$M=\frac{166.08}{0.37537}\approx442$

Answer:

$442$