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Compound interest and the rule of 72
Watch interest earn interest, and estimate how fast money doubles.
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Interest is what a bank pays you for keeping your money there, or what you pay to borrow. Compound interest means you also earn interest on your interest. The first year, you earn interest on what you put in. The next year, you earn interest on that plus last year's interest. Over decades, that snowball does most of the work.
The rule of 72 is a shortcut: divide 72 by the yearly interest rate to estimate how many years it takes money to double. At 6%, that's 72 ÷ 6 = 12 years.
Words to know
Write what each word means in your own words.
- Interest
- Compound interest
- Interest rate
Questions
- You put $1,000 in an account that pays 6% a year, compounded once a year. Finish the table. Round to the nearest cent.
Year Start of year Interest (6%) End of year 1 $1,000.00 $60.00 $1,060.00 2 $1,060.00 3 4 5 - With simple interest, you'd earn 6% of the original $1,000 every year. How much would you have after 5 years? How much more did compounding earn?
- Using the rule of 72, about how many years does it take money to double at each rate?
Yearly rate Years to double 3% 8% 12% - Maya invests $100 a month from age 16 to 26, then stops. Leo invests $100 a month from age 26 to 65. Both earn 7% a year. Who has more at 65?
- Maya, even though she put in about a quarter as much
- Leo, because he put in almost four times as much
- They end up with exactly the same amount
- Neither, because the money doesn't grow
- In your own words, why does starting early matter more than how much you start with?
Answer key: Compound interest and the rule of 72
Words to know
- Interest: The price of borrowing money. Borrowers pay it, and savers earn it.
- Compound interest: Interest you earn on your interest. Over time, it makes savings grow faster and faster.
- Interest rate: Interest shown as a percent of the amount borrowed or saved, usually per year.
Questions
- Year 2: $63.60, ending at $1,123.60. Year 3: $67.42, ending at $1,191.02. Year 4: $71.46, ending at $1,262.48. Year 5: $75.75, ending at $1,338.23.
- $1,000 + 5 × $60 = $1,300. Compounding earned $1,338.23 − $1,300 = $38.23 more.
- 3%: 24 years. 8%: 9 years. 12%: 6 years.
- A. Maya puts in $12,000 and ends with about $263,000. Leo puts in $46,800 and ends with about $244,000. Maya's money had ten extra years to compound. Try it at thedime.news/resources/start-early/.
- Answers will vary. Look for the idea that time lets interest earn interest, so early dollars grow far more.
The Dime worksheets are licensed under CC BY-NC 4.0. Share and adapt them freely with credit to The Dime, but don't sell them.
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