Question

tash is looking to take out a mortgage for $640,000 from a bank offering a monthly interest rate of 0.375%. using the formula below, determine her 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 values

$P = 640000$, $r=0.00375$, $n = 30\times12=360$

Step2: Substitute into formula

$M=\frac{640000\times0.00375}{1-(1 + 0.00375)^{-360}}$

Step3: Calculate denominator

Let $x=(1 + 0.00375)^{-360}=\frac{1}{(1 + 0.00375)^{360}}$. Using a calculator, $(1 + 0.00375)^{360}\approx3.0995$. So $x=\frac{1}{3.0995}\approx0.3226$. Then $1-(1 + 0.00375)^{-360}=1 - 0.3226 = 0.6774$.

Step4: Calculate numerator

$640000\times0.00375 = 2400$

Step5: Calculate $M$

$M=\frac{2400}{0.6774}\approx3543$

Answer:

$3543$