Question

Your credit card has an APR of 12.5%. What is your monthly interest rate and annual effective interest rate with monthly compounding? What would a balance of $2,000 grow to be if you skipped payments for 2 months?

Answer 1

Answer:

• Monthly interest rate: 1.04%

• Annual effective interest rate: 13.2%

• Balance of $2,000 if you skipped for two months: $2,041.88

Explanation:

1. What is your monthly interest rate and annual effective interest rate with monthly compounding?

The montly interest rate is the rate that is indeed applied every month.

It is the APR (annual percentage rate) divided by 12.

Thus, your montly interest rate for credit card that has an APR of 12.5% is:

• Monthly interest rate = 12.5% / 12 = 0.0125 / 12 ≈ 0.0104167 ≈ 1.042%

The annual effective rate is the compounded interest over a year:

• 1 + 0.0104167 = 1.0104167

• 1.0104167 × 1.0104167 . . . (twelve times)

• (1.0104167)¹² ≈ 1.1324

• 1.1324 - 1 = 0.1324 = 13.2%

2. What would a balance of $2,000 grow to be if you skipped payments for 2 months?

You have to add the interests of two months calculated with the compounding formula:

• $2,000 (1 + i)ⁿ = $2,000 (1 + 0.0104167)²

• $2,000 (1.0104167)² = $2,041.88