Free classroom resource · Suggested for grades 9–12
Compound interest lesson and worksheet
A short comparison activity for seeing how simple interest, annual compounding, and monthly compounding change the same starting balance. Includes a printable student page and a worked answer key.
Created by the Snowballr Editorial Team and published by Snowballr, a free ad-supported financial education site. See About Snowballr.
Teacher setup
Learning goals
- Calculate and compare simple and compound balances.
- Explain how earned interest can also earn interest.
- Distinguish a nominal annual rate from an effective annual yield.
Materials and timing
Paper and a calculator or spreadsheet. Allow about 25–35 minutes for prediction, calculations, discussion, and the exit question. Students can work alone or in pairs.
Set up the comparison
Each example starts with $1,000 and uses a fixed 6% nominal annual rate for three years. There are no extra deposits or withdrawals, fees, or taxes. The fixed rate is for practicing the math; it is not a forecast or a quoted financial product.
Simple interest
Balance = P × (1 + r × t)
Annual compounding
Balance = P × (1 + r)t
Monthly compounding
Balance = P × (1 + r/12)12t
P is the starting principal, r is 0.06, and t is the number of years. With monthly compounding, the periodic rate is 0.06 ÷ 12 = 0.005.
Student worksheet
Name: ____________________________________ Date: __________________
1. Predict before calculating
Which method do you think will have the largest balance after three years? What do you expect to happen to the differences over time?
2. Calculate the balance at the end of each year
Round each answer to the nearest cent.
| End of year | Simple interest | Annual compounding | Monthly compounding |
|---|---|---|---|
| 1 | |||
| 2 | |||
| 3 |
3. Explain the result
- At the end of year one, why are the simple-interest and annual-compounding balances equal?
- By the end of year three, how much larger is the annual-compounding balance than the simple-interest balance?
- Why does the monthly-compounding balance differ from annual compounding even though both use a 6% nominal annual rate?
4. Exit question
A $500 balance earns 4% nominal annual interest compounded monthly for two years. There are no deposits or withdrawals. What is the ending balance? How would the answer differ if 4% were an effective annual yield (APY) instead?
Instructor answer key
Worked answers
The balances below use the same principal, nominal rate, timing, and compounding conventions as the worksheet.
| End of year | Simple interest | Annual compounding | Monthly compounding |
|---|---|---|---|
| 1 | $1,060.00 | $1,060.00 | $1,061.68 |
| 2 | $1,120.00 | $1,123.60 | $1,127.16 |
| 3 | $1,180.00 | $1,191.02 | $1,196.68 |
- After year one, simple interest and annual compounding both reach $1,060.00; the annual interest is calculated on the original principal in both cases.
- After year three, annual compounding is $11.02 above simple interest. In year two, the annual-compounding balance earns an additional $3.60 because year-one interest remains in the balance.
- Monthly compounding applies interest each month, so interest credited earlier can earn interest later in the same year. At a 6% nominal rate, the model's effective annual rate is 6.17% when compounded monthly.
- The exit question is $541.57 at 4% nominal compounded monthly. At a 4% effective annual yield, the two-year result is $540.00. APY already includes annual compounding, so applying the monthly formula directly to 4% APY would treat the rate as nominal and produce a different result.
Sources and assumptions
The worksheet is an original practice activity. Its fixed-rate examples use the same monthly growth convention as Snowballr's compound interest calculator; they exclude recurring contributions, fees, taxes, inflation, and changes in rate. Results are arithmetic examples, not predictions or product comparisons.
- Investor.gov: What is compound interest? — official classroom explanation of interest-on-interest and student activities.
- CFPB: APY calculation rules — official disclosure rules used for the nominal-rate versus APY distinction in the exit question.
Reuse and license
This original lesson page, worksheet text, tables, and answer key are available under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. You may copy or adapt them with attribution: “Compound Interest Lesson and Worksheet, Snowballr, https://snowballr.io/compound-interest-lesson, CC BY 4.0.” Investor.gov and CFPB materials remain subject to their own terms; this license does not grant rights to third-party content, Snowballr software, or underlying source material.