Question

casey is looking to take out a mortgage for $200,000 from a bank offering an annual interest rate of 4.2%. compounded monthly. using the formula below, determine his monthly payment, to the nearest dollar, if the loan is taken over 30 years.

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

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

Explanation:

Step1: Identify the values

$P = 200000$, the annual interest rate is $4.2\%=0.042$, so the monthly interest rate $r=\frac{0.042}{12}=0.0035$, and the number of payments $n = 30\times12 = 360$.

Step2: Substitute into the formula

$M=\frac{P\times r}{1-(1 + r)^{-n}}=\frac{200000\times0.0035}{1-(1 + 0.0035)^{-360}}$.
First, calculate $(1 + 0.0035)^{-360}\approx0.29997$.
Then, $1-(1 + 0.0035)^{-360}=1 - 0.29997=0.70003$.
And $200000\times0.0035 = 700$.
So $M=\frac{700}{0.70003}\approx999.96\approx1000$.

Answer:

$1000$