The best way to understand compound interest is to see it in everyday situations. Here are six short examples, each worked out in full. All use the same formula:
A = P × (1 + r/n)n × t
P is the starting amount, r the annual rate as a decimal, n the number of times interest is added per year, and t the number of years.
1. A savings account
You put $5,000 in a savings account paying 4.5% compounded monthly and leave it for 5 years.
A = 5,000 × (1 + 0.045/12)60 = 5,000 × 1.251796 = $6,258.98. Interest: $1,258.98.
2. A fixed deposit or certificate
A 2-year deposit of $5,000 pays 4.5% compounded quarterly.
A = 5,000 × (1 + 0.045/4)8 = 5,000 × 1.093625 = $5,468.12. Interest: $468.12.
3. Credit card debt
You owe $3,000 on a card charging 22% APR, compounded monthly, and make no payments for a year (ignoring fees).
A = 3,000 × (1 + 0.22/12)12 = $3,730.79. The debt grows by $730.79 — an effective 24.36%. Compounding works against borrowers just as powerfully as it works for savers.
4. Saving $100 a month
You save $100 at the end of every month for 5 years at 5%, compounded monthly.
FV = 100 × [(1 + 0.05/12)60 − 1] ÷ (0.05/12) = $6,800.61. You deposited $6,000, so interest added $800.61.
5. Doubling your money
How long does money take to double at 8% compounded annually?
Exact: t = ln 2 ÷ ln 1.08 = 9.01 years. The Rule of 72 gives 72 ÷ 8 = 9 years — almost spot on.
6. Comparing two rates over 20 years
$10,000 at 4% vs 6%, compounded annually, for 20 years:
- At 4%: 10,000 × 1.0420 = $21,911.23
- At 6%: 10,000 × 1.0620 = $32,071.35
A 2-point difference in the rate produces about 85% more interest ($22,071 vs $11,911).
What the examples show
- Over a few years, compounding adds a modest amount (examples 1 and 2).
- High rates make compounding powerful — dangerously so on debt (example 3).
- Regular saving plus compounding builds wealth steadily (example 4).
- Small differences in rate become big differences over decades (example 6).
Try them yourself
Each example can be reproduced in our calculators: examples 1–3 and 6 in the Compound Interest Calculator, example 4 in the regular contributions calculator, and example 5 in the Time to Double Money Calculator. For the method behind them, read How to Calculate Compound Interest.