Question

You charged $1,000 on your credit card for Christmas presents. Your credit card company charges you 24% annual interest, compounded monthly. If you make the minimum payments of $25 per month, how long (in years) will it take to pay off your balance?

Answer 1

We can use the present value of annuity formula to calculate the no.of months it will take to pay off credit card balance.
Present value of annuity = P * {[1 - (1+r)^-n]/r}
Present value of annuity = credit card balance as on now = $1000
P = Credit card monthly payment = $25
r = rate of interest per month = 24%/12 = 2%
n = no.of months = ?
1000 = 25 * {[1 - (1+0.02)^-n]/0.02}
40 = [1 - (1+0.02)^-n]/0.02
0.80 = 1 - (1+0.02)^-n
1.02^-n = 0.20
n = 81.29
Total months required to pay off credit card balance = 81.29 months
No.of years required to pay off credit card balance = 81.29 months / 12 = 6.77 years