Question

# Barry has bought a new car and requires a loan of 12000 to pay for it....

Barry has bought a new car and requires a loan of 12000 to pay for it. The car dealer offers Barry two alternatives on the loan:

a) Monthly payments for 3 years, starting one month after purchase with an annual interest rate of 12% compounded monthly, or

b) Monthly payments for 4 years, also staring one month after purchase, with annual interest rate 15%, compounded monthly.

Find Barry's monthly payment and the total amount paid over the course of the repayment period under each of the two options.

Formula for calculating interest compounded monthly is

A= P * ((1+r/n) ^ (n *t))

where A is the amount calculated based on the compounded interest

"r" is the rate of compound interest

"n" is the number of times compounded in a year

"t" is the total number of years

"P" is the principal amount

Solution

First Option:

Amount=12000 * ((1+(12/100)/12)^(12 * 3))

Amount= 12000 * ((1+(.12/12) ^ 36))

Amount=12000 * (1.01 ^ 36)

Amount=12000 * 1..431

Amount=17,172.00

Therefore interest paid=17,172.00-12,000.00=5,172.00

Therefore EMI per month=17172/36=477

Second Option:

Amount=12000 * ((1+15/100)^(12 *4))

Amount= 12000 * ((1+(.15/12) ^ 48))

Amount=12,000 * (1.0125 ^ 48)

Amount=12,000 * 1.815

Amount=21,780

Therefore interest paid=21,780.00-12,000.00=9,180.00

Therefore EMI per month=21780/48=453.75