Question

Assume that you have a credit card that charges 17% interest annually with a minimum payment of 2% each month. If you have a balance of $5,000, you pay the minimum payment each month, and you make no other purchases with the card, what is your balance after 1 year? After 2 years? After 5 years? 


(Please show every step. No excel work)

Answer 1

APR = 17% annually so , monthly interest rate = 17/12 = 1.41%

Minimum payment is 2% each month = 2% of 5000 = $100

So the interest calculated is 100 ( 1.0141)^{n x 12} = 5000

n = 8.16 years so it will take 8 years approx to pay the amount

To calculate the balance after 1 year :

Interest Payment made in year 1: 100 (1.041)¹² = $161.96

Balance remaining = 5000 - 161.96 = $4,838.03

Interest Payment made in 2 years : 100 ( 1.041)²⁴ = $262.31

Balance remaining after 2 years = 5000 -262.31 = $4737.6

Interest Payment made in 5 years : 100 ( 1.041)⁶⁰ = $1114.40

Balance remaining after 5 years = 5000 - 1114.40 = $3885.59