Question

qasim is looking to take out a mortgage for $290,000 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 20 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: Calculate the monthly interest rate

The annual interest rate is $4.2\%=0.042$. So the monthly interest rate $r=\frac{0.042}{12}=0.0035$.

Step2: Calculate the number of payments

The loan is taken over 20 years. Since there are 12 months in a year, the number of payments $n = 20\times12=240$.

Step3: Identify the principal amount

The amount borrowed $P = 290000$.

Step4: Substitute values into the formula

$M=\frac{290000\times0.0035}{1-(1 + 0.0035)^{-240}}$.
First, calculate $(1 + 0.0035)^{-240}\approx0.4354$.
Then, $1-(1 + 0.0035)^{-240}=1 - 0.4354 = 0.5646$.
And $290000\times0.0035 = 1015$.
So $M=\frac{1015}{0.5646}\approx180$.

Answer:

$180$