Compound Interest: Money That Makes Money
Interest is money paid to you for letting your money be used. Compound interest pays interest on your interest.
$1,000 growing 8% a year becomes about $2,160 in 10 years and about $10,060 in 30 years — without adding a cent.
The Rule of 72: divide 72 by the yearly rate to estimate how many years it takes to double. 72 ÷ 8 = 9 years.
Time matters more than amount. Starting at 16 instead of 26 can more than double your result.
You, imagine you put your birthday money into a savings account. With compound interest, next year the bank won't just pay you interest on your original deposit, but also on the interest you earned this year!
Learning objective
Calculate compound growth, distinguish a hypothetical return from a promise, and recognize how fees, inflation and debt affect the result.
Understand the mechanism
Simple interest is calculated on the original amount. Compound interest is calculated on the growing balance, so previous interest becomes part of the next calculation. For annual compounding, future value equals starting balance × (1 + annual rate) raised to the number of years. Rates must be decimals: 5% is 0.05, not 5.
A bank savings rate and an investment return are not interchangeable. A savings account may offer a stated rate subject to its terms; stocks can rise or fall unpredictably. A constant 8% illustration is a mathematical scenario, not a forecast. Real investment returns arrive unevenly, and losses early or late can matter when you make contributions or withdrawals.
Compounding also works against you. Unpaid interest on debt can increase the amount on which later charges are calculated, depending on the contract. Compare borrowing costs with uncertain investment returns before deciding that investing while carrying expensive debt is automatically wise.
Put it to work
Separate three drivers: the amount you start with, how much you add and how long it grows. Regular contributions can matter more than hunting for a spectacular return. Automating a manageable contribution creates consistency, but keep short-term essential money out of volatile investments.
Fees reduce the return you retain; inflation reduces what the resulting money buys. If your account grows 5% while prices rise 3%, the approximate purchasing-power growth is 2%, before taxes. The exact real return is 1.05 ÷ 1.03 − 1, or about 1.94%.
The Rule of 72 estimates doubling time at a steady positive rate. It is useful for mental arithmetic, not proof of future market performance. When comparing products, check risk, fees, access to money and any restrictions, not just a headline rate.
Worked example
- 1
Start with $200 and assume 5% annual growth, no fees, no tax and no extra deposits.
- 2
After year one: $200 × 1.05 = $210. The $10 gain is now part of the balance.
- 3
After year two: $210 × 1.05 = $220.50. The second gain is $10.50, not $10.
- 4
After ten years: $200 × 1.05^10 ≈ $325.78. Simple interest would give $300, so $25.78 comes from growth on previous growth.
- 5
Rule of 72: 72 ÷ 5 ≈ 14.4 years to double. At a lower retained rate, doubling takes longer.
Show the assumptions alongside the number. Compounding rewards time, but no example guarantees a return.
Your practice lab
Calculate $500 growing at a hypothetical 4% for two years. Compare it with simple interest. Then explain why you would not put next month's transport money into stocks to earn that return.
Personal scratchpad · not graded or saved
The Tale of Two Savers
Liam started investing at age 16. He put aside $50 a month into an account that hypothetically earned an average of 8% per year. He did this for 10 years and then stopped adding money, letting his investment of $6,000 grow on its own.
His friend Chloe waited until she was 26 to start. To try and catch up, she invested $100 a month—twice as much as Liam—and continued investing for the next 20 years, also earning 8%. She invested a total of $24,000.
When they both reached age 46, they compared accounts. Even though Chloe had invested four times as much money, Liam's account was worth more. His smaller, earlier investment had an extra 10 years to compound and grow, demonstrating the incredible power of time.
Starting to invest early, even with small amounts, can be more powerful than starting later with larger amounts because it gives your money more time to compound.
Illustrative example — names and figures are composites for teaching.
The Rule of 72 helps you see how fast money can grow. Choose a realistic savings goal for your first venture (e.g., startup costs, new equipment). If you invested that amount at a hypothetical 8% per year, how long would it take to double? What does this tell you about the power of starting now?
Example: My goal is to save $500 for a better camera for my video business. If I invest it at 8%, the Rule of 72 (72 ÷ 8) says it would take about 9 years to double to $1,000 without me adding more. This shows me that if I start now, my money can do a lot of the work for me over time.
Go deeper — outside resources
- Compound Interest Calculator · U.S. Securities and Exchange Commission
- MyMoney.gov — learning hub · MyMoney.gov
- Introduction to Compound Interest · Khan Academy
Key ideas
- Interest on interest
- Rule of 72 estimates doubling time
- Starting early beats starting big
Try it: Using the Rule of 72, how long to double money at 6%?
Quick check
1. At 12% a year, roughly how long to double?
2. What is the biggest advantage a teen investor has?
3. If you invest $100 at 10% annual interest, what makes compound interest different from simple interest after the first year?
4. Your investment account grew by 7%, but inflation was 3%. What happened to your purchasing power?
5. Maya saved $500 for a school trip in three months. Her friend suggests investing it in the stock market to 'make it grow.' Why might this be a bad idea?
6. How does compound interest work when you have debt, like a credit card balance?