Question

lamonte is looking to take out a mortgage for $410,000 from a bank offering a monthly interest rate of 0.4%. using the formula below, determine his monthly payment, to the nearest dollar, if the loan is taken over 10 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 the values of $P$, $r$, and $n$

$P = 410000$, $r=0.004$, $n = 10\times12=120$

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

$(1 + 0.004)^{120}\approx1.612226$

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

$410000\times0.004\times1.612226=410000\times0.006448904 = 2644.05064$

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

$1.612226 - 1=0.612226$

Step5: Calculate $M$

$M=\frac{2644.05064}{0.612226}\approx4319$

Answer:

$4319$