An annual percentage rate, also known as APR, represents the sum of the periodic interest rates over the course of one year, but it does not account for the effects of compound interest. In order to accurately calculate the interest earned when interest compounds quarterly, you need to compute the annual percentage yield, or APY. You receive higher interest returns with quarterly compounding than annual compounding, because the interest you receive after the first quarter begins immediately accruing additional interest for the rest of the year.
In order to calculate compounded quarterly interest rates, you will need to divide the annual interest rate into four equal parts and then adjust the sum to reflect the quarterly compounding.
Getting Started With Quarterly Interest Rates
To get started, you'll need to know the annual interest rate you're earning on your account. This should be on the paperwork you've received from your lender or on your online account. If you can't find the information, your financial institution should be able to get it for you. You'll also need a calculator.
Divide Annual Interest Rate
Once you have that information, divide the annual interest rate by 4 to find the quarterly interest rate. For example, if the annual interest rate equals 4.04 percent, divide 0.0404 by 4 to get a quarterly interest rate of 0.0101. Add 1 to the quarterly interest rate. In this example, add 1 to 0.0101 to get 1.0101. Raise the sum to the fourth power, because interest compounds four times per year. In this example, raise 1.0101 to the 4th power to get 1.041.
Determine the Annual Percentage Yield
Subtract 1 from the result to find the annual percentage yield (APY) when interest is compounded quarterly. In this example, subtract 1 from 1.041 to find the APY equals 0.041, or about 4.1 percent.
Multiply the APY by the balance of the account to calculate the annual interest paid on the account. For example, if you had a savings account paying 4.04 percent interest, compounded quarterly, with $4,600 in the account, multiply $4,600 by 0.04102 to find you would earn $188.69 in interest over a year.
Using the Information Available
Once you've seen the difference between quarterly compounded interest and annual compounded interest, make sure you know what your own bank offers. If you're already thinking about switching due to a competing lender offering quarterly compounding, this calculation may give you the information you need to approach your current bank and see what they can do for you. They may be able to switch you to a different type of account, especially if it means keeping you as a valued customer.
- DePaul University: Compound Interest Formula
- Compound Interest Calculator | Investor.gov
- Continuously Compounded Interest Formula and Calculator
- Federal Deposit Insurance Corporation. "Appendix A to Part 1030—Annual Percentage Yield Calculation." Accessed July 26, 2020.
- U.S. Securities and Exchange Commission. "What Is Compound Interest?" Accessed July 26, 2020.
- American Express. "APY vs. APR: The Basics About How Interest Is Calculated." Accessed July 26, 2020.
- Consumer Financial Protection Bureau. "What Is a Credit Card Interest Rate? What Does APR Mean?" Accessed July 26, 2020.
- Consumer Financial Protection Bureau. "What Is the Difference Between a Mortgage Interest Rate and an APR?" Accessed July 26, 2020.
- University of Wisconsin. "Cheat Sheet 2," Page 1. Accessed July 26, 2020.
Based in the Kansas City area, Mike specializes in personal finance and business topics. He has been writing since 2009 and has been published by "Quicken," "TurboTax," and "The Motley Fool."