Question

You receive a credit card application from Shady Banks Savings and Loan offering an introductory rate of 2.7 percent per year, compounded monthly for the first six months, increasing thereafter to 17.6 percent compounded monthly. Assuming you transfer the $13,000 balance from your existing credit card and make no subsequent payments, how much interest will you owe at the end of the first year? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Here we need to find the FV of a lump sum, with a changing interest rate. We must do this problem in two parts. After the first six months, the balance will be:

FV = $13,000[1 + (0.027 / 12)]⁶

FV = $13,176.49

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

FV = $13,176.49[1 + (0.176 / 12)]⁶

FV = $14,379.38

The problem asks for the interest accrued, so, to find the interest, we subtract the beginning balance from the ending balance. The interest accrued is:

Interest = $14,379.38 - $13,000

Interest = $1,379.38