Guide
Simple vs compound interest
The two formulas side by side, how far apart they drift over time, and which one your loan or savings account actually uses.
Simple interest is charged only on the original amount. Compound interest is charged on the original amount plus whatever interest has already accrued. Over a year the difference is negligible; over a decade it decides the outcome.
The two formulas
| Simple | Compound | |
|---|---|---|
| Interest | I = P × r × t | I = P(1 + r/n)^(nt) − P |
| Final amount | A = P(1 + rt) | A = P(1 + r/n)^(nt) |
| Shape of growth | A straight line | A curve that steepens |
| Interest earned each year | The same every year | Larger every year |
The structural difference is in the exponent. Simple interest multiplies by time; compound interest raises to the power of time.
How far apart they drift
$10,000 at 6%:
| Years | Simple | Compound (annual) | Difference | Compound is ahead by |
|---|---|---|---|---|
| 1 | $10,600 | $10,600 | $0 | 0% |
| 3 | $11,800 | $11,910 | $110 | 0.9% |
| 5 | $13,000 | $13,382 | $382 | 2.9% |
| 10 | $16,000 | $17,908 | $1,908 | 11.9% |
| 20 | $22,000 | $32,071 | $10,071 | 45.8% |
| 30 | $28,000 | $57,435 | $29,435 | 105.1% |
At one year they are identical — compounding has had nothing to compound yet. At thirty years compound interest has produced more than double. The divergence is slow at first, which is exactly why it is easy to dismiss.
Which one applies to you
| Product | Interest type | Note |
|---|---|---|
| Savings accounts | Compound | Usually daily or monthly compounding |
| Certificates of deposit / fixed bonds | Compound | Often quoted as an APY, which already includes compounding |
| Credit cards | Compound | Daily compounding, which is why balances grow quickly |
| Mortgages and car loans | Compound in structure | Amortised, so the interest is on the declining balance |
| Most personal loans | Simple | Interest on the outstanding principal, no interest-on-interest |
| Government bond coupons | Simple | Unless you reinvest the coupons, which makes it compound |
| Payday and short-term loans | Flat | Charged on the original sum for the whole term regardless of repayment |
That last row is the one to watch. A flat-rate loan charges interest on the original amount even as you repay it, so the effective rate is close to double the quoted one. A "10% flat" loan over a year is roughly 18–19% APR, because on average you only had half the money.
Why simple interest can favour the borrower
On a loan, simple interest is generally better for you. Because interest never accrues on unpaid interest, paying early reduces the total directly, and there is no compounding penalty for a late month beyond the interest itself.
The reverse holds for savings. On money you are lending to a bank, you want compounding — and as frequently as you can get it, though as the table below shows, frequency is a much smaller lever than the rate itself.
APR and APY: the same rate, described differently
| APR | APY (or AER) | |
|---|---|---|
| Includes compounding | No | Yes |
| Usually quoted on | Loans | Savings |
| 12% compounded monthly | 12% APR | 12.68% APY |
The convention is not accidental. Loans are advertised with the smaller-looking number and savings with the larger one. To compare two products honestly, convert both to the same basis:
APY = (1 + APR/n)^n − 1
Worked example: the same $5,000 both ways
At 8% over three years:
| Year | Simple — interest | Simple — balance | Compound — interest | Compound — balance |
|---|---|---|---|---|
| 1 | $400.00 | $5,400.00 | $400.00 | $5,400.00 |
| 2 | $400.00 | $5,800.00 | $432.00 | $5,832.00 |
| 3 | $400.00 | $6,200.00 | $466.56 | $6,298.56 |
A difference of $98.56 after three years. Extend the same figures to twenty years and simple interest gives $13,000 against compound's $23,305 — the gap has grown from two percent of the balance to nearly eighty.
Compare both on your figures
Open the Simple Interest Calculator