Question

How long will it take to pay off a loan of ​$51000 at an annual rate of 12 percent compounded monthly if you make monthly payments of ​$650​? Use five decimal places for the monthly percentage rate in your calculations.

Answer 1

Answer:

Given,

The present value of the loan, P.V. = $ 51,000,

Annual rate of interest = 12 %,

So, the rate per month, r = $\frac{12}{12}$ = 1 % = 0.01,

Also, the monthly payment, P = $ 650,

Let n be the number of months,

Since, monthly payment of a loan is,

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

$650=\frac{51000(0.01)}{1-(1+0.01)^{-n}}}$

By graphing calculator,

$n=154.299447759\approx 154.29944$

Hence, it will take approximately 154 months to pay off the loan.