Question

You receive a credit card application from Shady Banks Savings and Loan offering an introductory rate of 3.7 percent per year, compounded monthly for the first six months, increasing thereafter to 18.6 percent compounded monthly. Assuming you transfer the $18,000 balance from your existing credit card and make no subsequent payments, how much interest will you owe at the end of the first year?

Answer 1

Here we need to find the FV of a lump sum, with a changing interest rate. After the first six months, the balance will be:

FV = $18,000[1 + (0.037 / 12)]^6

FV = $18,335.5775

This is the balance in six months. The FV in another six months will be:

FV = $18,335.5775[1 + (0.186 / 12)]^6

FV = $20,108.24

To find the interest, we subtract the beginning balance from the ending balance. The interest accrued is:

Interest owed = $20,108.24 - $18,000

Interest owed = $2,108.24