Simple vs compound interest
Updated on June 18, 2026 · by Rafael Rossi
The difference between simple and compound interest fits in one sentence: with simple interest, the rate always applies to the original amount; with compound interest, it applies to the current balance. It sounds like an academic distinction. Over twenty years it multiplies the result by three.
The two formulas
Simple interest: A = P × (1 + i × n)
Compound interest: A = P × (1 + i)n
Where P is the principal, i the rate per period and n the number of periods. The only visible difference is where the n sits: multiplying, or in the exponent. That change of position is what turns a straight line into a curve.
The comparison, in numbers
$10,000 at 12% a year, under both regimes:
| Term | Simple interest | Compound interest | Difference |
|---|---|---|---|
| 1 year | $11,200 | $11,200 | $0 |
| 2 years | $12,400 | $12,544 | $144 |
| 5 years | $16,000 | $17,623 | $1,623 |
| 10 years | $22,000 | $31,058 | $9,058 |
| 20 years | $34,000 | $96,463 | $62,463 |
| 30 years | $46,000 | $299,599 | $253,599 |
Three things worth reading out of that table:
- In the first period the two regimes give exactly the same answer. There is no accumulated interest yet to compound on. That is why, for very short terms, the distinction is irrelevant.
- After two years the gap is barely 1%. Nearly invisible — and that is precisely why intuition gets trained wrong: in everyday timeframes, the two regimes look alike.
- Over twenty years, compound delivers 2.8 times the simple result. Same principal, same rate, same term.
Time to double
Another way to see it: at 12% a year, money under simple interest takes exactly 100 months — 8 years and 4 months — to double, because 8.33 × 12% = 100%. Under compound interest it takes 6.1 years.
And unlike the simple regime, compound doubles again every 6.1 years. Simple interest would need another 16.7 years to quadruple; compound needs 6.1 more.
Where each one shows up in real life
- Compound interest: essentially everything involving time. Mortgages, auto loans, credit cards, personal loans, savings accounts, CDs, bonds, retirement accounts.
- Simple interest: some auto loans and personal loans are written as "simple interest loans", where interest accrues daily on the outstanding principal and is not added back into the balance; also late-payment penalties and certain short-term notes.
The practical rule: assume compound unless the contract explicitly says otherwise. When a lender advertises a rate and shows a fixed monthly payment, the math behind it is an amortising schedule, not a simple division.
Beware the multiplication test
It is tempting to check a loan by multiplying the rate by the number of payments. It does not work, and it errs in the direction that misleads.
Take $10,000 at 2% a month over 24 payments. The naive multiplication suggests 2% × 24 = 48%, or $4,800 in interest. The real figure on an amortising schedule is $2,689 — a payment of $528.71, $12,689 in total.
Why less? Because you do not owe the full $10,000 for 24 months. Each payment retires part of the principal, and the next month's interest applies to a smaller balance. The multiplication would only hold if you paid nothing until the end — and in that case, compounding would put the debt at $16,084, not $14,800.
The moral cuts both ways: mental arithmetic overstates the cost of an amortising loan and understates the cost of a debt that rolls unpaid. Both distortions pull intuition the wrong way.
The number that settles it: APR
To compare offers, look past the advertised rate to the APR, which US lenders are required to disclose. It folds the interest rate together with points, origination fees and certain closing costs into a single percentage — and it regularly reveals that the offer with the lowest headline rate is not the cheapest one.
Frequently asked questions
Does a savings account pay simple or compound interest? Compound. Interest is credited periodically and becomes part of the balance, earning interest itself from then on. That is exactly what the APY figure describes.
Which regime is better? For a saver, compound, with no argument. For a borrower it is the reverse: debt under compounding grows on its own, and the higher the rate, the faster.
What is a "simple interest loan"? One where interest accrues on the outstanding principal and is never capitalised into it. Pay early in the month and less interest accrues; pay late and more does. It is genuinely different from a compounding balance, which is why paying a few days early can save real money on these.
Why is simple interest still taught first? Because it is the conceptual foundation, and because it still applies in real short-term situations. But it should be made clear that it is the exception, not the rule — teaching that stops at simple interest leaves students unprepared for the contract they will actually sign.