Question

Phoebe realizes that she has charged too much on her credit card and has racked up $5,500 in debt. If she can pay $250 each month and the card charges 12 percent APR (compounded monthly), how long will it take her to pay off the debt? Time to pay off debt: ___ months

Answer 1

Present value of " n " months payment of 250 each must be equal to 5500

250 * [ 1 - ( 1 +r)^-n ] / r = 5500

r = 0.12 / 12 months = 0.01 and n = number of months ( to be calculated)

250 * [ 1 - (1.01)^-n ] / 0.01 = 5500

[ 1 - (1.01)^-n ] = 5500 * 0.01 / 250 = 0.22

- (1.01)^-n = 0.22 - 1 = - 0.78

Cancel negative on both sides and take log on both sides

- n * Log (1.01) = Log (0.78)

- n * 0.004321373 = - 0.107905397

n =  0.107905397 / 0.004321373

= 24.97 ............ or 25 months