Simple vs Compound Interest: The Difference in Real Dollars
Simple vs compound interest explained with both formulas, a $10,000 side-by-side over 20 years, and where each one shows up in real financial products.
Simple interest pays on your original deposit. Compound interest pays on your deposit and on every dollar of interest it has already earned. Over a year the difference is trivial. Over twenty years it is the difference between a decent return and a transformed balance.
The two formulas
Simple interest: A = P × (1 + r × t)
Compound interest: A = P × (1 + r/n)^(n×t)
Where P is principal, r the annual rate as a decimal, t the years, and n the compounding periods per year.
Side by side: $10,000 at 6% for 20 years
Simple: 10,000 × (1 + 0.06 × 20) = 10,000 × 2.20 = $22,000
Compound annually: 10,000 × 1.06^20 = 10,000 × 3.2071 = $32,071
Same principal, same rate, same period. The gap is $10,071 — more than the original deposit — and every dollar of it comes from interest earning interest.
| Year | Simple | Compound (annual) | Gap |
|---|---|---|---|
| 1 | $10,600 | $10,600 | $0 |
| 5 | $13,000 | $13,382 | $382 |
| 10 | $16,000 | $17,908 | $1,908 |
| 15 | $19,000 | $23,966 | $4,966 |
| 20 | $22,000 | $32,071 | $10,071 |
| 30 | $28,000 | $57,435 | $29,435 |
Note the shape: the gap is nearly invisible for the first five years, then accelerates. That is why compounding feels like it does nothing until suddenly it does everything.
Compounding frequency
More frequent compounding helps, but with sharply diminishing returns. The same $10,000 at 6% for 20 years:
| Compounding | Final balance |
|---|---|
| Annual (n=1) | $32,071 |
| Quarterly (n=4) | $32,907 |
| Monthly (n=12) | $33,102 |
| Daily (n=365) | $33,198 |
Moving from annual to monthly gains about $1,031. Moving from monthly to daily gains $96. The frequency matters far less than the rate and the years.
Where each one actually appears
Simple interest shows up in:
- Most car loans and personal instalment loans (interest accrues on the outstanding balance, not on unpaid interest)
- Bonds paying periodic coupons that you do not reinvest
- Short-term promissory notes and many payday-style products
Compound interest shows up in:
- Savings accounts, CDs, and money market accounts
- Credit card balances — compounded daily, which is why a carried balance grows faster than the stated APR suggests
- Retirement accounts and reinvested dividend portfolios
- Student loans where unpaid interest capitalises onto the principal
The asymmetry is worth naming: compounding works for you in the savings column and against you in the debt column. A credit card at 22% compounded daily has an effective annual rate near 24.6%.
FAQ
Is compound interest always better than simple interest? Better when you are earning it, worse when you are paying it. On a loan, simple interest costs less for the same nominal rate.
How do I know if my loan uses simple or compound interest? Check whether unpaid interest can capitalise. Standard amortising mortgages and auto loans charge interest on the remaining balance each period and do not compound unpaid interest as long as you pay on schedule.
What rate turns $10,000 into $50,000 in 20 years? About 8.4% compounded annually: 1.084^20 ≈ 5.0. The Rule of 72 gives a fast sanity check — 72 ÷ 8.4 ≈ 8.6-year doubling, and 20 years covers just over two doublings plus change.
Run both scenarios yourself with the Simple Interest Calculator and the Compound Interest Calculator. For the mechanics behind the exponent, read the compound interest formula explained.
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*See the gap open up on your own numbers: use the Compound Interest Calculator.*