When does interest start earning interest?
Compare simple and compound interest and explain how the same growth can help a saver or increase an unpaid debt.
Start with a fictional $1,000 balance. Interest is added once at the end of each year at a constant rate. There are no deposits, withdrawals, repayments, fees, taxes, or defaults. Read the ending balance as savings owned, or as debt owed if all interest is capitalized and no payments are made.
Print creates the fixed example worksheet below. “Print with teacher answers” adds a separate answer page. Use your browser’s Save as PDF option to download it.
Change one assumption.
Predict what will happen, adjust an input, then use the results to check your reasoning. Sliders work with arrow keys.
What the numbers mean
After 5 years, $469.33 has been added to the original balance by compound interest. For savings this is interest earned; for the no-payment debt scenario it is interest owed. The simple-interest comparison adds $400.
Show calculation table
| Year | Compound balance ($) | Simple balance ($) |
|---|---|---|
| 0 | 1,000 | 1,000 |
| 1 | 1,080 | 1,080 |
| 2 | 1,166.4 | 1,160 |
| 3 | 1,259.71 | 1,240 |
| 4 | 1,360.49 | 1,320 |
| 5 | 1,469.33 | 1,400 |
Use the terms precisely.
Open a term to read its meaning, then use it in your explanation.
Principal
The starting amount saved or borrowed.
Simple interest
Interest calculated only on the original principal: P × r × years.
Compound interest
Interest added to the balance earns or accrues further interest: ending balance = P × (1 + r)^years.
Interest rate versus APR
A quoted interest rate alone may omit costs. APR is a broader borrowing-cost measure; this simplified model does not calculate a regulated APR.
- Principal
- The starting amount saved or borrowed.
- Simple interest
- Interest calculated only on the original principal: P × r × years.
- Compound interest
- Interest added to the balance earns or accrues further interest: ending balance = P × (1 + r)^years.
- Interest rate versus APR
- A quoted interest rate alone may omit costs. APR is a broader borrowing-cost measure; this simplified model does not calculate a regulated APR.
Work through the starting example.
These questions use the default settings, even if you changed the interactive lab. Show your calculations and explain one assumption behind your answer.
Starting inputs: Starting balance: $1,000; Annual interest rate: 8%; Years: 5 years.
Name: __________________________ Date: ______________
- At the defaults, calculate the compound balance after one year and after five years.
- Compare the five-year compound balance with simple interest. How much is due to compounding beyond simple interest?
- Reset, then set the rate to 0%. Explain both results. Why would a loan with monthly repayments behave differently from this model?
Try a new case
Compare 10 and 20 years at the same rate. Does doubling time double the interest? Use the figures to support your answer.
Exit ticket
What changed, what stayed fixed, and which term helps explain the result?
A 35 minute teaching plan
Use 5 minutes to introduce the question and vocabulary, 10 to predict and test inputs in pairs, 12 for the worksheet, 5 to compare explanations, and 3 for the exit ticket. Without devices, use the printed starting case and calculate changes by hand.
Look for a correct calculation, precise terminology, and an explanation that respects the model’s limits. For the open challenge, accept different cases when the arithmetic and reasoning support them.
Open teacher answer key
- Year 1: 1000 × 1.08 = $1,080. Year 5: 1000 × 1.08^5 = $1,469.33, including $469.33 of interest.
- Simple ending balance = 1000 × (1 + 0.08 × 5) = $1,400. Compounding adds $69.33 beyond simple interest.
- Both balances remain $1,000 at zero interest. Loan repayments reduce the outstanding balance; interest timing, fees, and contract terms also matter. The no-payment model does not represent a normal amortizing loan.
Teacher answer key: Interest, saving & borrowing
- Year 1: 1000 × 1.08 = $1,080. Year 5: 1000 × 1.08^5 = $1,469.33, including $469.33 of interest.
- Simple ending balance = 1000 × (1 + 0.08 × 5) = $1,400. Compounding adds $69.33 beyond simple interest.
- Both balances remain $1,000 at zero interest. Loan repayments reduce the outstanding balance; interest timing, fees, and contract terms also matter. The no-payment model does not represent a normal amortizing loan.
For the challenge and exit ticket, credit correct calculations, a clearly stated assumption, and precise use of a relevant term. Different supported examples are acceptable.
Where the model stops
These are mathematical scenarios, not promised savings returns or loan quotes. Many debts use different accrual rules and require regular payments.
Further reading: CFPB: how compound interest works. These fictional activities are original to World Economy. Reference links do not imply endorsement.
World Economy · losttofound.org/classroom/labs/compound-interest. An adult educator may print or privately share this free activity with their own learners. Keep the source attached. No resale or public rehosting.