You charged $1,000 on your credit card for Christmas presents. Your credit card

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?

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? 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?

Explanation / Answer

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

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