Question

Today the average undergraduate student is responsible for paying off a ​$3,750 balance on​ his/her credit card. Suppose the monthly interest rate is 1.25​%​ (15​%​APR). How many months will it take to repay the​ $3,750​ balance, assuming monthly payments of​ $150 are made and no additional expenses are charged to the credit​ card?

How many months will it take to repay the initial balance?

Please show all work.

Answer 1

Loan amount = 3750

interest rate = 1.5% per month = 0.015

Monthly payment = 150

let no. of months be n

then we use the formula

A = P *[i((1 + i)^n)/((1 + i)^n-1)]

putting values into the equation

150 = 3750 * [0.015*((1 + 0.015)^n)/((1 + 0.015)^n-1)]

0.04 = [0.015*((1.015)^n)/((1.015)^n-1)]

0.015*(1.015)^n = 0.04 * ((1.015)^n-1)

0.015*(1.015)^n = 0.04 * (1.015)^n - 0.04

(0.04 - 0.015)*(1.015)^n = 0.04

0.025*(1.015)^n = 0.04

(1.015)^n = 0.04/0.025 = 1.6

n = log1.6 / log 1.015 = 31.57 months