Compound vs Simple Interest
Two very different ways to calculate interest — and over long horizons, the gap between them is enormous. Here's how each one works, when it applies, and what the difference looks like in real dollars.
The Short Version
Simple interest is calculated only on the original principal. The interest payment is the same every period.
Compound interest is calculated on the principal plus all previously accrued interest. The interest payment grows every period because the base grows.
Same rate, same time, very different outcome. The longer the horizon, the more the two diverge.
The Formulas
Simple interest
A = P × (1 + r × t)
Interest each year: P × r (always the same)
Compound interest (annual compounding)
A = P × (1 + r)t
Interest each year: previous balance × r (grows every year)
Where P = principal, r = annual rate (as a decimal), t = time in years.
Side-by-Side: $10,000 at 7% Over Time
| Year | Simple Interest | Compound Interest | Difference |
|---|---|---|---|
| 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 |
Annual compounding assumed for the compound column.
When Each Type Applies
Simple Interest Is Used For
- Most mortgages (US daily-accrual)
- Auto loans
- Personal loans and student loans
- Many short-term bonds and Treasury bills
Compound Interest Is Used For
- Savings accounts and money market accounts
- Certificates of deposit (CDs)
- 401(k), IRA, and brokerage accounts
- Credit card balances (compounded daily)
- Reinvested dividends and bond interest
Why the Compound Gap Grows
In year one, both methods earn the same interest because the base is identical. From year two onward, compound interest starts earning interest on the interest it earned last year — and that effect snowballs. By year 30 of the example above, compound interest is growing by about $5,000 per year just from interest on prior interest. That's why time horizon matters more than rate for long-term savers.
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Frequently Asked Questions
What is the main difference between compound and simple interest?
Simple interest is calculated only on the original principal. Compound interest is calculated on the principal plus any interest already earned. Over time, compound interest produces exponentially larger returns because every interest payment becomes part of the new base.
Is compound interest always better than simple interest?
For savers and investors, yes — compound interest produces more growth. For borrowers, simple interest is better because it caps interest at the principal balance and doesn't accumulate on top of itself. Mortgages and car loans typically use simple interest; credit cards and savings accounts use compound interest.
What types of accounts use compound interest?
Savings accounts, money market accounts, certificates of deposit (CDs), retirement accounts (401k, IRA), brokerage accounts, and credit card balances all use compound interest. The compounding frequency varies — daily, monthly, quarterly, or annually.
How much faster does compound interest grow than simple interest?
Over 10 years at 7% on $10,000, simple interest yields $17,000 while compound interest yields $19,672 — a $2,672 difference. Over 30 years, simple interest yields $31,000 while compound interest yields $76,123 — the gap balloons to $45,123 because each year's gains compound on top of previous gains.
Do mortgages use simple or compound interest?
US mortgages use simple interest, calculated daily based on the outstanding principal. Each monthly payment covers the accrued interest first, then reduces the principal. Because the principal balance shrinks every month, less interest accrues over time, even though the rate stays the same.