Effective Interest Rates — Practice Questions

By Kenneth Boyd, Kate Mooney

When you borrow money, and the interest is charged more often than annually, this is called compounding. As a result, the effective interest rate will be more than the annual rate.

The following practice questions require you to calculate the effective rate of loans where the interest is compounded quarterly.

Practice questions

Use the following information to answer the questions.

Travel Fridge, Inc. borrows $45,000 from the bank for one year at an annual rate of 8% compounded quarterly.

  1. How much interest will the company pay on this loan?

  2. What is the effective rate of the loan?

Answers and explanations

  1. $3,709.45

    If the interest is compounded quarterly, then interest is charged at the rate of 2% every 3 months. And, the unpaid interest is added to the principal.

    First 3 months:

    image0.png

    in interest is added to the principal.

    Second 3 months:

    image1.png

    in interest is added to the principal.

    Third 3 months:

    image2.png

    in interest is added to the principal.

    Fourth 3 months:

    image3.png

    in interest is due.

    image4.png

  2. 8.243%

    The effective rate is equal to the interest actually paid divided by the principal. If the interest is compounded quarterly, then interest is charged at the rate of 2% every 3 months. And, the unpaid interest is added to the principal.

    First 3 months:

    image5.png

    in interest is added to the principal.

    Second 3 months:

    image6.png

    in interest is added to the principal.

    Third 3 months:

    image7.png

    in interest is added to the principal.

    Fourth 3 months:

    image8.png

    in interest is due.

    image9.png

    total interest paid.

    image10.png

    or 8.243%

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