# 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.

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- **Canonical URL:** https://dothecalculation.com/blog/finance/simple-vs-compound-interest-comparison
- **Category:** Finance
- **Author:** Do The Calculation Team
- **Published:** 2026-08-03
- **Reading time:** 10 min read
- **Publisher:** Do The Calculation (https://dothecalculation.com)
- **Methodology:** https://dothecalculation.com/methodology

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## 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.

Tool: [Try the compound interest calculator](https://dothecalculation.com/calculators/compound-interest-calculator) — Model a balance with any compounding frequency and regular contributions, and see the interest-on-interest share separately.

## The two formulas

**Simple and compound interest**

```
Simple: A = P(1 + rt)    ·    Compound: A = P(1 + r/n)^(nt)
```
- P is principal, r the annual rate as a decimal, t years, n compounding periods per year.
- Simple interest grows in a straight line. Compound interest grows in a curve.

## The gap over time

$10,000 at 6%, with nothing added and nothing withdrawn. Compounded annually against simple interest at the same rate.

**$10,000 at 6%: simple against annually compounded**
| 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.

> **Where the extra money comes from** — At year 30 the account has earned $47,435 of interest. Only $18,000 of that is interest on your original $10,000. The remaining $29,435 is interest earned by earlier interest.

## 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:

**Compounding frequency, same rate and term**
| 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.

**Converting a nominal rate to an effective one**

```
APY = (1 + APR/n)^n − 1
```
- 19.99% APR compounded daily: (1 + 0.1999/365)^365 − 1 = 22.13%
- Savings products advertise APY because it is the larger number. Loans advertise APR for the same reason.

## 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

**Which interest applies where**
| 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 |

> **Capitalisation is the trap** — A simple-interest loan can behave like a compound one if unpaid interest is added to the principal. That is what capitalisation means on a student loan after a deferment, and it is why a balance can grow while payments are paused.

## 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.

Tool: [Try the interest calculator](https://dothecalculation.com/calculators/interest-calculator) — Compare 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.

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_Source: [Do The Calculation](https://dothecalculation.com/blog/finance/simple-vs-compound-interest-comparison). Quote freely with attribution and a link to this page._