Question

Suppose you have accumulated $20,000 in credit card debt. If the interest rate on the credit card is 20.1% APR compounded monthly, how many years will it take you to pay off this debt if you pay $500 per month? (Answer to the nearest tenth of a year)

Answer 1

Credit Card Debt Accumulate = PV = $20,000

r = interest rate = 20.1%/12 = 1.675%

Let n = number of months

P = Monthly payment = $500

The following formula is used to calculate the number of months to pay off the debt

Monthly payment = [r.PV] / [1 - (1+r)^-n]

$500 = [$20,000 * 1.675%] / [1 - (1+1.675%)^-n]

$500 = $335 / [1 - (1.01675)^-n]

1 - (1.01675)^-n = 0.67

(1.01675)^-n = 0,33

(1.01675)^n = 3.03030303

n = 66.741 months

n = 66.741 months / 12 = 5.56175 years

Therefore, it will take 5.56 years to payoff the credit card debt