Simple vs Compound Interest: The Gap, in Actual Numbers
Simple interest is charged on the original principal only. Compound interest is charged on interest too. Over ten years the difference is modest; over thirty it is most of the money.
Simple vs Compound Interest
Simple interest is calculated on the original principal every period. Compound interest is calculated on the principal plus all interest already added. That single difference is why a modest sum left alone for thirty years becomes a large one, and why a credit card balance you keep paying the minimum on barely moves.
Try the compound interest calculatorModel a balance with any compounding frequency and regular contributions, and see the interest-on-interest share separately.The two formulas
The gap over time
$10,000 at 6%, with nothing added and nothing withdrawn. Compounded annually against simple interest at the same rate.
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| Years | Simple interest | Compound interest | Difference |
|---|---|---|---|
| 1 | $10,600 | $10,600 | $0 |
| 5 | $13,000 | $13,382 | $382 |
| 10 | $16,000 | $17,908 | $1,908 |
| 20 | $22,000 | $32,071 | $10,071 |
| 30 | $28,000 | $57,435 | $29,435 |
| 40 | $34,000 | $102,857 | $68,857 |
The two are identical after one year and separated by more than the original principal after thirty. Nothing about the rate changed. The curve is doing all the work, and it barely moves in the first few years, which is exactly why compounding is easy to underrate while you are young enough to benefit from it.
How much compounding frequency matters
More frequent compounding pays more, but the gains shrink quickly and converge on a ceiling. $10,000 at 6% for 10 years:
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| Frequency | n per year | Balance after 10 years | Effective annual rate |
|---|---|---|---|
| Annually | 1 | $17,908 | 6.000% |
| Semi-annually | 2 | $18,061 | 6.090% |
| Quarterly | 4 | $18,140 | 6.136% |
| Monthly | 12 | $18,194 | 6.168% |
| Daily | 365 | $18,221 | 6.183% |
| Continuously | ∞ | $18,221 | 6.184% |
Moving from annual to monthly is worth $286 over a decade. Moving from monthly to daily is worth $27. Chasing compounding frequency is rarely where the decision lies; the rate and the time horizon dominate everything else.
APR and APY are the same distinction
APR is the nominal annual rate, ignoring compounding within the year. APY, sometimes called effective annual rate, includes it. A card advertising 19.99% APR compounded daily has an effective rate near 22.1%, which is what you actually pay.
The rule of 72, and when it stops working
Divide 72 by the annual rate to approximate the years to double. At 6%, 72 / 6 = 12 years; the exact figure is 11.90. At 8%, the rule says 9 years against an exact 9.01.
It is accurate between roughly 4% and 12% and drifts outside that band. At 2% it says 36 years against an exact 35.0; at 25% it says 2.88 against an exact 3.11. Treat it as a mental check rather than a calculation.
Where you will meet each in practice
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| Product | Typically | Note |
|---|---|---|
| Savings accounts | Compound | Usually daily or monthly, quoted as APY |
| Credit cards | Compound | Daily on the average balance, which is why balances persist |
| Most car loans | Simple | Interest accrues on the outstanding balance, not on interest |
| US federal student loans | Simple, daily accrual | But unpaid interest can capitalise into principal |
| Certificates of deposit | Compound | Frequency stated in the terms |
| Bonds | Simple coupons | Compounding only if you reinvest the coupons yourself |
What follows from all this
For saving, time matters more than rate. $200 a month for 30 years at 6% reaches about $201,000, of which $72,000 was contributed. The same $200 a month for 15 years reaches about $58,000. Halving the horizon cost far more than half the outcome.
For borrowing, the same asymmetry works against you, which is why an extra payment early in a mortgage removes interest for the entire remaining term and an identical payment in the final years removes almost none.
Try the interest calculatorCompare simple and compound interest side by side on the same principal, rate, and term.Which is better, simple or compound interest?
It depends which side you are on. When saving, compound interest is better because your interest earns interest. When borrowing, simple interest is cheaper for the same rate and term.
How much difference does daily versus monthly compounding make?
Very little. On $10,000 at 6% over ten years, daily compounding beats monthly by about $27. Rate and time horizon matter far more than frequency.
Is the rule of 72 accurate?
It is close between about 4% and 12%. At 6% it gives 12 years against an exact 11.90. Outside that band the error grows, so use it as a sanity check rather than for planning.
Do car loans use compound interest?
Most US car loans use simple interest, accrued daily on the outstanding balance. Because the balance falls as you pay, paying early in the month reduces the interest charged, and extra payments go straight to principal.
Written by
Do The Calculation Team
Do The Calculation
Do The Calculation is built by a small team of data analysts and spreadsheet developers. Where a guide depends on a published formula, standard, or government rule, the calculator it links to names that source directly so you can check the number yourself.
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