Question

Mitchell took out a loan for $1100 at a 19.2% APR, compounded monthly, to

buy a scanner. If he will make monthly payments of $71.50 to pay off the
loan, how many total payments will he have to make?

A. 16

B. 19

C. 18

D. 17​

Answer 1

C. 18

Explanation:

We can find the numbers of payments using following formula

PV = PMT(1- (1+r)^-n)/r

PVr / PMT = 1 - (1+r)^-n

Where

PV = present value = $1,100

PMT = monthly payments = $71.50

r = interest rate = 19.2% / 12 = 1.6%

n = numbers of month = ?

Placing values in the formula

(1+r)^-n = 1 - PVr /PMT

1.016^-n = 1-1100 x 0.016/71.50

1.016^-n = 0.753846154

-n x log 1.016 = log 0.753846154

n = - log 0.753846154 /log 1.016

n = 17.8

n = 18 payments