Compound Interest Explained: The Formula, Examples, and Why It Matters
Albert Einstein allegedly called compound interest "the eighth wonder of the world." Whether he said it or not, the math behind the quote is real — compound interest is one of the most powerful forces in personal finance, working for you when you save and against you when you borrow.
Simple vs Compound Interest
Before compound interest, there's simple interest — the baseline for comparison.
Simple interest is calculated only on the original principal:
I = P × r × t
Where P = principal, r = annual rate (decimal), t = time in years.
Compound interest is calculated on the principal plus accumulated interest. Each period, interest earns interest:
A = P × (1 + (r) / (n))^(n × t)
Where:
- A = final amount
- P = principal (initial investment)
- r = annual interest rate (decimal)
- n = number of times interest compounds per year
- t = time in years
Worked Example
Scenario: You invest $10,000 at 7% annual interest for 20 years.
Simple interest:
- I = 10,000 × 0.07 × 20 = $14,000 in interest
- Total = $24,000
Compound interest (compounded monthly, n=12):
- A = 10,000 × (1 + 0.07/12)^(12×20)
- A = 10,000 × (1.005833)^240
- A = 10,000 × 4.0387
- **Total =
$40,387** — nearly $16,000 more than simple interest
Compounding Frequency Matters
The more frequently interest compounds, the more you earn. Here's how the same $10,000 at 7% for 10 years looks under different compounding schedules:
| Compounding | Final Value | Difference vs Annual |
|-------------|------------|----------------------|
| Annual (n=1) | $19,672 | — |
| Quarterly (n=4) | $19,890 | +$218 |
| Monthly (n=12) | $19,935 | +$263 |
| Daily (n=365) | $19,954 | +$282 |
The differences are real but modest at 10 years. They become significant over 30–40 year investment horizons.
The Rule of 72
A simple mental shortcut: divide 72 by the annual interest rate to estimate how many years it takes to double your money.
- At 6%: 72 ÷ 6 = 12 years to double
- At 8%: 72 ÷ 8 = 9 years to double
- At 10%: 72 ÷ 10 = 7.2 years to double
The rule works because ln(2) ≈ 0.693, and for rates between 5–10%, the approximation error is under 1%.
Compound Interest Against You: Debt
Compound interest works identically in reverse when you're borrowing. Credit card debt compounding at 20% annually doubles in just 3.6 years if you make no payments.
Example: $5,000 on a credit card at 20% APR with no payments:
- Year 1: $6,000
- Year 2: $7,200
- Year 3: $8,640
- Year 5: $12,442
This is why minimum payment traps are so effective — minimum payments often barely cover monthly interest, leaving the principal almost unchanged.
Factors That Maximise Compound Growth
Time is the most important variable. Starting 10 years earlier is worth more than doubling your contribution amount. A person who invests $5,000/year from age 25–35 (10 years, then stops) often ends up with more at 65 than someone who invests the same annual amount from age 35–65 (30 years).
Rate matters enormously over long periods. The difference between 6% and 8% returns over 30 years on $10,000 is:
- 6%: $57,435
- 8%: $100,627
A 2% improvement more than doubles the outcome.
Avoid interrupting compounding. Withdrawing early resets the compounding clock. Even small withdrawals have outsized long-term costs.
Real APY vs Nominal Rate
When a bank advertises "5% interest compounded monthly," the actual return (APY — Annual Percentage Yield) is slightly higher:
APY = (1 + (r) / (n))^n - 1
At 5% compounded monthly: APY = (1 + 0.05/12)^12 - 1 = 5.116%
When comparing savings accounts, always compare APY, not the nominal rate.
Calculate Compound Interest Now
Our compound interest calculator lets you adjust the principal, rate, compounding frequency, and term to see exactly how your money grows — with a year-by-year breakdown.