credit card APR

Question

Assume that you have a balance of $4000 on your Discover credit card and that you make no more charges. Assume that Discover charges 27% APR and that each month you make only the minimum payment of 3% of the balance.

What will the balance be after 12 years? (Round your answer to the nearest cent.)

Answer 1

Here's the formula for time: I figured 62.082 or 63 months. As for the payments I used $120=3% of 4000.

Remember 3%=.03 and 27%=.27.

The formula for the credit card equation is:

       N=−1/30*ln(1+b/p(1−(1+APR/365)^30))

/(ln(1+APR/365))

where:

1. N = number of months to payoff the credit card
2. APR = credit card annual interest rate
3. b = balance of the credit card
4. p = monthly payment to be made

Answer 2

The APR is 27% or 0.27 written as a proportion. On a monthly basis, the APR is 0.27/12 = 0.0225. This is how much interest increases each month.

But, every month the minimum 3%, or 0.03 is paid. So the change in the balance of the principal, $4000, is 0.0225 - 0.03 = -0.0075.

Twelve years is the same as 12*12 = 144 months.

Therefore, the balance after 12 years is $4000*(1 - 00.0075)¹⁴⁴ = $4000*(0.9925)¹⁴⁴

= $4000*0.338216 = $1352.86