Question

You charged $4200 on your credit card for holiday gifts. Your credit card company charges you 8% annual interest, compounded monthly. If you make the minimum payments of $65 per month, how long will it take (to the nearest month) to pay off your balance?

Answer 1

Using present value of annuity formula , we can calculate the no.of months required to pay off the credit card balance.
Present value of annuity = P * {[1 - (1+r)^-n]/r}
Present value of annuity = present credit card balance = $4200
P = Monthly payment = $65
r = rate of interest per month = 8%/12 = 0.006667
n = no.of months required = ?
4200 = 65 * {[1 - (1+0.006667)^-n]/0.006667}
64.61538 = [1 - 1.006667^-n]/0.006667
0.430769 = 1 - 1.006667^-n
0.56923 = 1.006667^-n
n = 84.80
No.of months required to pay off the credit card balance = 85 months