Question

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.

Answer 1

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