The difference sounds technical. Over 30 years, it's the difference between tripling your money and making it ten times bigger.
The two formulas
Simple interest: interest only on the original amount.
A = P × (1 + r × t)
Compound interest: interest on the original amount and on interest already earned.
A = P × (1 + r/n)^(n × t)
| Letter | Meaning |
|---|---|
| A | final amount |
| P | starting amount |
| r | annual rate as a decimal (8% = 0.08) |
| t | years |
| n | compounding periods per year (1 yearly, 4 quarterly, 12 monthly) |
Same money, both ways
100,000 at 8% a year:
| Years | Simple | Compound yearly | Compound monthly |
|---|---|---|---|
| 1 | 108,000 | 108,000 | 108,300 |
| 5 | 140,000 | 146,933 | 148,985 |
| 10 | 180,000 | 215,892 | 221,964 |
| 20 | 260,000 | 466,096 | 492,680 |
| 30 | 340,000 | 1,006,266 | 1,093,573 |
Notice:
- For the first few years, the gap is small.
- By year 30, compounding gives about 3× what simple interest does.
- Monthly vs yearly compounding matters much less than time.
Try your own numbers in the Compound Interest Calculator.
Why compounding curves upward
With simple interest you earn 8,000 every year, forever. With compounding, year 1 earns 8,000, but year 2 earns 8% of 108,000, which is 8,640. Year 20 earns 8% of about 400,000, which is nearly 32,000. The interest itself starts earning interest.
Compounding frequency and the effective rate
A bank might quote "8% compounded quarterly". The effective annual rate tells you what you really earn in a year:
effective rate = (1 + r/n)^n − 1
| Compounding | Effective annual rate at 8% |
|---|---|
| Yearly | 8.00% |
| Quarterly | 8.24% |
| Monthly | 8.30% |
| Continuous | 8.33% |
When you compare savings accounts or deposits, compare the effective rates.
The Rule of 72
To estimate how long it takes money to double:
years to double ≈ 72 ÷ annual rate (%)
| Rate | Doubles in about |
|---|---|
| 4% | 18 years |
| 6% | 12 years |
| 8% | 9 years |
| 12% | 6 years |
At 8% the exact answer is 9.006 years, so the shortcut is close. It works best between about 6% and 10%.
It works for costs too: at 6% inflation, prices double in about 12 years.
When it works against you
Compounding is just as powerful on debt:
- Credit cards compound unpaid balances, often monthly, at high rates.
- Unpaid loan interest that gets added to the balance (capitalised) starts charging interest itself. That's common with student loans. See Student Loan Interest.
Most EMI loans are reducing balance: interest is charged on what you owe each month and paid off as you go, so it doesn't snowball. See How to Calculate EMI.
Three takeaways
- Start early. Time matters more than the rate or how often interest compounds.
- Compare effective rates, not headline rates.
- Pay off compounding debt first, before investing at a lower rate.