Compound Interest vs. Simple Interest: Formula, Examples, Key Differences

By the CalcWise editorial team · Updated September 26, 2026 · 8 min read

The simple interest formula

Simple interest is exactly what the name promises: interest calculated only on the original principal, every period, forever. The formula is:

A = P × (1 + r × t)

• A — the total amount (principal plus interest) at the end
• P — the principal, i.e., the starting amount (e.g., $10,000)
• r — the annual interest rate written as a decimal (5% = 0.05)
• t — the time the money is held, in years

Notice that time t appears as a plain multiplier, not an exponent. That means growth is linear: the balance rises by the same dollar amount each year. With $10,000 at 5% simple interest, you earn $500 every single year — year 1, year 10, year 20. The interest earned is I = P × r × t, so after 20 years you have earned $10,000 in interest, for a total of $20,000.

Because the growth is a straight line, simple interest is easy to compute by hand. That simplicity is also its defining limitation: it never benefits from growth-on-growth.

The compound interest formula

Compound interest is calculated on the principal plus all previously accumulated interest. The formula is:

A = P × (1 + r/n)^nt

• A — the total amount at the end
• P — the principal (e.g., $10,000)
• r — the annual rate as a decimal (5% = 0.05)
• n — how many times interest compounds per year (1 = annually, 12 = monthly, 365 = daily)
• t — time in years

The critical difference is the exponent nt. Because time sits in the exponent, growth is exponential: slow at first, then accelerating. With $10,000 at 5% compounded annually, year 1 earns $500, year 2 earns $525, year 3 earns $551.25 — each year's interest is bigger because the balance it is calculated on is bigger. The U.S. Securities and Exchange Commission's investor.gov glossary defines this as interest earned on both the initial principal and the accumulated interest from prior periods.

If you are making regular contributions rather than a single deposit, the companion formula is the future value of an annuity — our Compound Interest Calculator handles that case.

Side by side: $10,000 at 5% for 20 years

Start with $10,000, leave it untouched for 20 years at 5%, and compare what each formula produces:

Three observations from the table:

1. They start identical. In year 1, both methods earn exactly $500, because there is no prior interest to compound yet. Compounding needs time to pull ahead.
2. The lead grows with time. By year 20, the compound balance earns $1,263 in a single year — more than double the $500 that simple interest still pays.
3. Compounding frequency adds a little extra. Monthly compounding (n = 12) beats annual compounding by about $593 over 20 years. A nice bonus, but the frequency matters far less than the rate and the time horizon.

Here is the balance every five years, so you can see the curve bend upward:

The "Gap" row tells the whole story: a $263 difference after five years, a $6,533 difference after twenty. Compounding's advantage is small early and large late — which is exactly why starting early matters so much.

Where each one appears in real life

Knowing the formulas is useful; knowing which one applies to the contract in front of you is essential.

Simple interest in the wild:

• Many auto loans and personal loans. Lenders often compute interest on the original loan amount (or use amortizing schedules that behave simply). The interest you pay per period shrinks as the balance shrinks, and there is no interest-on-interest spiral on the original principal.
• Certain bonds and certificates of deposit. Some fixed-income products pay coupon interest that is not reinvested by default — you receive the interest as cash, so only the principal keeps earning.
• Short-term lending and payday-style loans. Fees and flat interest quoted on the borrowed amount often use simple math — though the effective rates are punishingly high, which is the real danger.

Compound interest in the wild:

• Savings accounts and money market funds. Interest is credited to the account and starts earning immediately — the classic compounding setup.
• Investment portfolios. Reinvested dividends and capital gains compound over time, which is why long-term stock returns behave like a compound-growth curve (with plenty of volatility along the way).
• Credit card debt and unpaid balances. This is compounding working against you: unpaid interest is added to the balance, and the next month's interest is charged on the larger amount. At 24% APR, a $5,000 balance left alone becomes roughly $6,340 in one year — and that is before late fees.
• Mortgages (in a different sense). Mortgage amortization schedules effectively compound the lender's return, since early payments are mostly interest on the full balance.

The practical rule: when you are saving or investing, you want compounding working for you — so reinvest interest and dividends rather than cashing them out. When you are borrowing, you want to avoid compounding working against you — so pay down high-interest balances before they snowball.

Compound vs. simple: the comparison table

If you only remember one thing from this comparison: simple interest grows in a straight line, compound interest grows in a curve that bends upward. Over short periods the difference is trivial; over decades it is life-changing. To see what that curve looks like with your own numbers — including regular monthly contributions — run them through our Compound Interest Calculator.

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