Question

Kraig deposited money into a money market account. It has an interest of 12% and is compounded annually. Kraig thought 3% would be the equivalent quarterly interest rate. Is Kraig correct? If he is, explain why. If he is not correct, state what the equivalent quarterly interest rate. Explain.

Answer 1

If the amount is P, with the interest rate of 12%, the interest over the year is:

• P*(1.12) - P = 0.12P

In this case the quarterly interest rate is:

• 0.12P/4 = 0.03P

With the same amount and 3% quarterly rate, the yearly interest would be:

• P*(1.03)^4 - P = 0.1255P

The quarterly interest rate in this case is:

• 0.1255P/4 = 0.031375P

If the quarterly interest rate is r, it should be little less than 3% to yield a 12% yearly rate.

So Kraig is wrong.