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 of variables

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

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

$(1 + 0.00375)^{180}\approx1.949328$

Step3: Calculate numerator

$Pr(1 + r)^n=420000\times0.00375\times1.949328\approx3092.23$

Step4: Calculate denominator

$(1 + r)^n-1=1.949328 - 1=0.949328$

Step5: Calculate monthly payment $M$

$M=\frac{3092.23}{0.949328}\approx3257$

Answer:

$3257$