How Simple Interest Works
Simple interest is calculated only on the original principal. Formula: I = P × r × t. On $10,000 at 7% for 5 years: I = $10,000 × 0.07 × 5 = $3,500. Total = $13,500. The $3,500 earned in Year 1 does not itself earn interest in subsequent years.
How Compound Interest Works
Compound interest is calculated on principal plus accumulated interest. Each period, the previous interest earns new interest. Formula: A = P(1 + r/n)^(nt). On the same $10,000 at 7% compounded annually for 5 years: A = $10,000 × (1.07)^5 = $14,026. Earned interest: $4,026 — $526 more than simple interest.
Simple vs. compound interest on $10,000 at 7% annual rate
| Year | Simple Interest Total | Compound Interest Total | Compound Advantage |
|---|---|---|---|
| 1 | $10,700 | $10,700 | $0 |
| 5 | $13,500 | $14,026 | $526 |
| 10 | $17,000 | $19,672 | $2,672 |
| 20 | $24,000 | $38,697 | $14,697 |
| 30 | $31,000 | $76,123 | $45,123 |
| 40 | $38,000 | $149,745 | $111,745 |
On $10,000 at 7% over 40 years: simple interest returns $38,000. Compound interest returns $149,745. The gap — $111,745 — was created entirely by reinvesting interest. This is why Einstein allegedly called compound interest the eighth wonder of the world.
Where Simple vs. Compound Interest Applies
Interest type by financial product
| Financial Product | Interest Type | Why |
|---|---|---|
| U.S. Treasury Bills | Simple (discount basis) | Short-term, single payment |
| Some personal loans | Simple | Interest doesn’t compound if paid monthly |
| Savings accounts | Compound (monthly/daily) | Interest reinvested automatically |
| Credit cards | Compound (daily) | Unpaid balance triggers compounding — very expensive |
| Mortgage loans | Compound (monthly) | Standard amortization formula |
| Certificates of Deposit | Compound | Interest added to principal each period |
| Bonds (coupon bonds) | Simple per period | Coupon is fixed, doesn’t compound unless reinvested |
When Compound Interest Works Against You
On the borrowing side, compound interest is your enemy. Credit card balances compounded daily at 24% APR: $5,000 left unpaid grows to $5,329 in 90 days without a single additional charge. After one year of no payments: $6,286. After five years: $14,842. This is why minimum payments on high-rate credit cards are financial quicksand.
See Compound vs. Simple on Your Numbers
Enter any amount and rate — see how compounding pulls ahead of simple interest over your time horizon.