Lesson 13: Compound Interest
Of all the ideas in personal finance, one matters more than any other for a young saver: compound interest. You met it briefly in Lesson 7. Now it is time to understand it fully, because it is the engine that turns small, regular savings into large sums over a lifetime — and, on the borrowing side, the force that turns small debts into crushing ones.
Compound interest means earning interest on your interest. With simple interest, you earn interest only on the original amount. With compound interest, each period's interest is added to the balance, and the next period's interest is calculated on the new, larger balance. Take an example: 100 units saved at 10% a year, compounded yearly — an example rate, not a real one; actual rates vary and change over time. After year one you have 110. After year two, 10% of 110 is 11, giving 121. After year three, 10% of 121 is 12.10, giving 133.10. Compare that with simple interest at the same rate: 110, 120, 130. The gap starts small — just 3.10 after three years — but it grows every year, because the amount earning interest keeps growing. After ten years, the simple-interest total is 200, while the compound total is about 259. The same rate, the same starting amount — and the difference is entirely due to compounding.
100 units at 10% a year: simple interest vs compound interest
Example only, at a 10% yearly rate: after 10 years the compound total is about 259 units, against 200 with simple interest. Real rates vary.
Time Is the Multiplier
Compounding rewards time more than it rewards large amounts. Starting ten years earlier matters more than saving twice as much later, because the early money has ten extra years of growth on growth. This is why the advice to start saving young is not a slogan but arithmetic. Regular small deposits help too: each deposit starts its own compounding journey, and the habit of adding to savings means the balance grows from both ends — new money in, and growth on everything already there. The rule of 72 gives a quick estimate: divide 72 by the yearly interest rate to find roughly how many years it takes for money to double. At an example rate of 10%, money doubles in about 7.2 years; at 6%, in about 12 years. It is only an approximation, but it shows why even modest rates, given enough time, are powerful.
The Other Edge of the Sword
Compounding is not always your friend. When you borrow money, compound interest works against you: unpaid interest is added to what you owe, and the next month's interest is charged on the larger amount. That is how credit card debt grows so fast when only minimum payments are made. The lesson is symmetrical: compounding rewards patient savers and punishes slow repayers. Understanding which side of it you are on is one of the most valuable things you can learn about money.
Key Terms
- Compound interest
- Interest calculated on the principal plus interest already earned, so growth speeds up over time.
- Simple interest
- Interest calculated only on the principal, so it grows by the same amount each period.
- Principal
- The original amount saved or borrowed, before interest is added.
- Compounding period
- How often interest is added to the balance — for example, yearly, monthly or daily.
- Rule of 72
- A quick estimate: divide 72 by the yearly interest rate to find roughly how many years it takes money to double.
- Growth on growth
- The effect where interest earned in earlier periods itself earns interest in later periods.
Discussion Questions
- Why does compounding reward starting early more than starting with a large amount?
- Using the rule of 72, how long would money take to double at an example rate of 8% a year? What does that tell you?
- Why is compound interest described as a double-edged sword?
Practice Questions
- What is the difference between simple interest and compound interest?
- You save 100 units at 10% compound interest per year. How much do you have after 2 years? After 3 years?
- At the same rate with simple interest, how much would you have after 10 years, and how does it compare with compound interest?
- What does the rule of 72 estimate, and what is the estimate at an example rate of 6%?
- Why does compound interest make unpaid credit card debt grow quickly?
Show answers
- Simple interest is charged only on the principal; compound interest is charged on the principal plus interest already earned. Compound growth speeds up over time.
- 121 after 2 years; 133.10 after 3 years. Year one: 100 + 10 = 110. Year two: 110 + 11 = 121. Year three: 121 + 12.10 = 133.10.
- 200 with simple interest, against about 259 with compound interest. Simple interest adds 10 each year (100 + 10 × 10 = 200); compounding adds interest on the growing balance.
- It estimates how many years it takes money to double: 72 divided by the yearly rate. At 6%, about 72 ÷ 6 = 12 years.
- Unpaid interest is added to what you owe, and interest is then charged on the larger amount. The debt grows on itself, faster and faster, when only minimum payments are made.