Simple against compound
Simple interest is charged only on the original principal. It grows in a straight line — the same amount every period, forever.
- A
- Final amount
- P
- Principal
- r
- Annual rate as a decimal
- t
- Time in years
Compound interest is charged on the principal plus all interest already added. The base grows, so each period earns more than the last, and the curve bends upward.
- n
- Compounding periods per year
Over short periods the difference is negligible. Over long ones it is the whole story. $10,000 at 5% for ten years earns $5,000 simple against $6,470 compounded monthly — and over thirty years, $15,000 against $34,673.
| Years | Simple | Compound | Difference |
|---|---|---|---|
| 1 | $10,500 | $10,512 | $12 |
| 5 | $12,500 | $12,834 | $334 |
| 10 | $15,000 | $16,470 | $1,470 |
| 20 | $20,000 | $27,126 | $7,126 |
| 30 | $25,000 | $44,677 | $19,677 |
Compounding frequency and APY
The more often interest compounds, the more you earn from the same nominal rate. The effective annual rate — APY — expresses this as a single comparable number.
| Frequency | Effective rate | $10,000 after 10 years |
|---|---|---|
| Simple (none) | 5.0000% | $15,000 |
| Annually | 5.0000% | $16,289 |
| Semi-annually | 5.0625% | $16,386 |
| Quarterly | 5.0945% | $16,436 |
| Monthly | 5.1162% | $16,470 |
| Daily | 5.1267% | $16,487 |
Note the diminishing returns. Going from annual to monthly adds $181 over ten years; going from monthly to daily adds only $17. The theoretical ceiling is continuous compounding, A = Pert, which on this example gives $16,487 — essentially the same as daily.
Where each type is used
| Product | Interest type |
|---|---|
| Savings accounts | Compound, usually daily or monthly |
| Fixed deposits (India) | Compound, quarterly |
| Certificates of deposit | Compound, varies by issuer |
| Mortgages and auto loans | Compound on the reducing balance |
| Credit cards | Compound daily — which is why balances grow fast |
| Most car title and payday loans | Simple, but at extreme rates |
| Treasury and corporate bonds | Simple — coupons paid, not reinvested automatically |
The asymmetry is worth noticing: compounding works for you in savings and against you in debt. A credit card at 22% compounded daily has an effective rate of 24.6%.
For savings with regular contributions, use the compound interest calculator. For loan repayment, the loan calculator.
Frequently asked questions
What is the difference between simple and compound interest?
Simple interest is calculated only on the original principal, so it grows linearly. Compound interest is calculated on the principal plus accumulated interest, so it grows exponentially.
On $10,000 at 5% for 30 years, simple yields $25,000 and monthly compounding yields $44,677.
What is APY and why does it differ from the interest rate?
APY is the effective annual rate after compounding is taken into account. A nominal 5% compounded monthly has an APY of 5.1162%, because each month's interest also earns interest.
APY is the number to compare accounts on, since it accounts for frequency.
Does daily compounding make much difference?
Less than most people expect. On $10,000 at 5% over ten years, daily compounding earns $17 more than monthly.
Going from annual to monthly matters more, adding $181 over the same period. Beyond monthly, the returns diminish sharply.
How long will it take my money to double?
Divide 72 by the annual rate for a close estimate. At 5% that is about 14.4 years; the exact figure with monthly compounding is 13.9 years.
The Rule of 72 is accurate to within a few months for rates between 5% and 12%.
Is interest income taxable?
In most jurisdictions, yes, as ordinary income in the year it is earned — even if you leave it in the account.
In India, banks deduct TDS above ₹50,000 of interest a year. In the US, interest over $10 is reported on Form 1099-INT.