Question

11. His friend Kyle grants him a loan of $ 5,000, instructing him to collect 18% interest payable at the end of (40) months using the compound interest method. Total interest and total to pay at the end of month 40.
a) $ 2,997, interest, total payable $ 7,997
b) $ 1,667 interest, total payable $ 3333
c) $ 4,070 interest, total payable $ 9,070
d) $ 3,000 interest, total payable $ 5,900
e) _______________________________

Answer 1

Solution:-

The loan is for 40 months at a rate of 18% per annum or 1.5% per month compounded monthly.

The formula for future value is as follows:

Future value= Principal*(1+r)ⁿ

where,

Principal= $5,000

r= rate of interest per period= 18%/12 months = 1.5% per month

n= number of periods of compounding= 40

Thus,

Future value= $5,000*(1+1.5%)⁴⁰

Future value= $5,000*1.814= $9,070

Therefore, total future value to be paid after 40 months is $9,070 and total interest is $4,070 (i.e. $9,070-$5,000).

Hence, the correct option is option c.