Question

Mary owes an amount of $1,460 on her credit card. The annual percentage rate (APR) is 3%, compounded monthly. Her minimum monthly payment is $20.

a. If she makes only this minimum payment, how long will it take to repay the card balance (assuming no more charges are made)?

b. If she makes the minimum payment plus $10 extra each month (for a total of $30), how long will it take to repay the card balance?

Answer 1

a. i = 3%/12 = 0.25% per month

Let no. of months required to pay off be n, then

20*(P/A,0.25%,n) = 1460

(P/A,0.25%,n) = 1460 / 20 = 73

((1 + 0.0025)^n-1)/(0.0025 *(1 + 0.0025)^n) = 73

((1.0025)^n-1)/(0.0025 *(1.0025)^n) = 73

(1.0025)^n - 1  = 73 * (0.0025 *(1.0025)^n)

(1.0025)^n - 1  = 0.1825 *(1.0025)^n)

(1.0025)^n = 1 / (1 - 0.1825) = 1.22324159

taking log both sides

n = log 1.22324159 / log 1.0025 = 80.70 months ~ 81 months

b.

i = 3%/12 = 0.25% per month

Let no. of months required to pay off be n, then

30*(P/A,0.25%,n) = 1460

(P/A,0.25%,n) = 1460 / 30 = 48.666667

((1 + 0.0025)^n-1)/(0.0025 *(1 + 0.0025)^n) = 48.666667

((1.0025)^n-1)/(0.0025 *(1.0025)^n) = 48.666667

(1.0025)^n - 1  = 48.666667 * (0.0025 *(1.0025)^n)

(1.0025)^n - 1  = 0.1216667 *(1.0025)^n)

(1.0025)^n = 1 / (1 - 0.1216667) = 1.138519924

taking log both sides

n = log 1.138519924 / log 1.0025 = 51.96 months ~ 52 months