Question

31. Calculating Interest Expense You receive a credit card application from
Shady Banks Savings and Loan offering an introductory rate of .9 percent
per year, compounded monthly for the first six months, increasing thereafter
to 18.5 percent compounded monthly. Assuming you transfer the $10,000
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, thebalance will be:

FV = $10,000[1 + (.009 / 12)]^6

FV = $10,045.08

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

FV = $10,045.08[1 + (.185 / 12)]^6

FV = $11,010.81

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

Interest owed = $11,010.81 - $10,045.08

Interest owed = $965.73