Question

Devin took out a 25-year loan for $70,000 at 8.7% interest, compounded monthly. What is his monthly payment?

A)$548.19
B)$573.12
C)$616.37
D)$533.16

Answer 1

The answer of this problem is :
B

Answer 2

B) $573.12

Explanation:

Since, the payment per period of a loan is,

`P=(r(P.V.))/(1-(1+r)^(-n))`

Where, P.V. is the principal amount,

r is the rate per period,

n is the number of periods,

Here, P.V. = $ 70,000,

Time = 25 years

Since, the payment is paid monthly,

And, 1 year = 12 months,

So, the number of periods, n = 12 × 25 = 300,

Also, the rate per year = 8.7 % = 0.087

So, the rate per month,

`r=(0.087)/(12)`

Hence, the monthly payment is,

`P=((0.087)/(12)(70000))/(1-(1+(0.087)/(12))^(-300))`

`=\$ 573.124525343\approx \$573.12`

Option B is correct.