Discover credit card APR

Question

Assume that you have a balance of $3500 on your Discover credit card and that you make no more charges. Assume that Discover charges 24% APR and that each month you make only the minimum payment of 3.5% of the balance.

Find a formula for the balance B after t monthly payments.

Answer 1

Original balance is $3500. APR is 24% or 0.24 as a proportion. Each month the interest increases by 0.24/12 = 0.02. The monthly payment is 3.5% or 0.035 as a proportion. The rate at which the interest changes each month is 0.02 - 0.035 = -0.015.

Thus at time t, expressed in months, the balance becomes $3500*(1-0.015)^t.

After 1 month, the balance is $3500(0.985)¹ = $3447.50.

After 12 months, it is $3500(0.985)¹² = $2919.46, to the nearest penny.

After 24 months it is $3500(0.985)²⁴ = $2435.22, and so on.