Question

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

Answer 1

The answer of this problem is :
 B

Answer 2

Answer:

B) $573.12

Step-by-step explanation:

Since, the payment per period of a loan is,

$P=\frac{r(P.V.)}{1-(1+r)^{-n}}$

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,

$r=\frac{0.087}{12}$

Hence, the monthly payment is,

$P=\frac{\frac{0.087}{12}(70000)}{1-(1+\frac{0.087}{12})^{-300}}$

$=\ 573.124525343\approx \ 573.12$

Option B is correct.