Question

ian is looking to take out a mortgage for $420,000 from a bank offering a monthly interest rate of 0.375%. using the formula below, determine his monthly payment, to the nearest dollar, if the loan is taken over 15 years.

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

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

Explanation:

Step1: Identify values

$P = 420000$, $r=0.00375$, $n = 15\times12=180$

Step2: Calculate $(1 + r)^n$

$(1 + 0.00375)^{180}\approx1.95479$

Step3: Calculate $Pr(1 + r)^n$

$420000\times0.00375\times1.95479 = 420000\times0.0073304625\approx3078.79425$

Step4: Calculate $(1 + r)^n - 1$

$1.95479- 1=0.95479$

Step5: Calculate $M$

$M=\frac{3078.79425}{0.95479}\approx3225$

Answer:

$3225$