Compound vs. Simple Interest: What Is the Difference?

The Two Formulas

Simple interest is computed only on the original principal. The interest owed or earned is I = P x r x t, and the ending amount is A = P(1 + rt), where P is principal, r the annual rate as a decimal, and t the time in years. The interest for each period is identical, so the balance grows in a straight line. Compound interest is computed on the principal plus whatever interest has already been added, giving A = P(1 + r/n)^(nt), where n is the number of compounding periods per year. Because each period's interest becomes part of the base for the next, the balance grows along a curve. Over a single period at the same stated rate the two produce the same result; the divergence appears only as periods accumulate.

A Worked Comparison

Take $10,000 at a stated 6 percent for 10 years, purely as arithmetic. Under simple interest the calculation is 10,000 x 0.06 x 10 = $6,000 of interest, for an ending amount of $16,000; each year contributes exactly $600. Under annual compounding the ending amount is 10,000 x 1.06 raised to the tenth power, which is approximately $17,908 — about $1,908 more, all of it interest earned on previously credited interest. Extend the term to 30 years and the gap widens sharply: simple interest gives $28,000, while annual compounding gives roughly $57,435. The comparison illustrates the structural point that the difference between the two methods is small over short horizons and becomes the dominant term over long ones.

Compounding Frequency and the Effective Rate

Within compound interest, the frequency matters. On $10,000 at a stated 6 percent for one year, annual compounding gives $10,600; semi-annual gives $10,609; quarterly, about $10,613.64; monthly, about $10,616.78; daily, about $10,618.31; and continuous compounding, using A = Pe^(rt), gives about $10,618.37. Each step raises the result, but by progressively less, converging on the continuous limit. This is why disclosure regimes separate the stated rate from the effective one: the annual percentage yield (APY) required on US deposit disclosures under the Truth in Savings Act incorporates within-year compounding, so two accounts quoting the same nominal rate but compounding at different frequencies show different APYs and can be compared directly.

Where Each Method Is Actually Used

Deposit accounts: Savings accounts and certificates of deposit generally compound, commonly daily or monthly, and are disclosed as an APY.
Credit cards: Revolving balances that are not paid in full typically accrue interest on the average daily balance with daily compounding, so the effective cost slightly exceeds the stated APR.
Many auto loans: Commonly structured as simple-interest loans, where interest accrues daily on the outstanding principal balance and does not compound, so the timing of a payment within the month affects how much of it reduces principal.
Amortising mortgages: Interest is charged each period on the remaining balance rather than compounding onto it, because the scheduled payment covers the accrued interest in full.
Some short-term instruments and bonds: Coupon interest is typically paid out rather than reinvested automatically, so any compounding depends on what is done with the coupon.

The Distinction That Matters Most

The practical difference between the two is not really the formula but what happens to interest once it is credited. Compounding occurs when interest is added to the base and left there. Anything that removes it — a coupon paid out and spent, a deposit withdrawn, a fee charged against the balance — converts part of the outcome back toward the simple-interest path. This is also why the phrase compound interest is used loosely for two different things: the crediting convention of a specific account, which is defined in its terms, and the general phenomenon of returns accumulating on returns, which depends on what is done with the proceeds. When comparing two disclosed offers, the comparable figures are APR for credit and APY for deposits, since each is defined to incorporate the relevant conventions.