Compound Interest vs. Simple Interest

Simple interest multiplies principal × rate × time, always on the original amount. Compound interest multiplies the growing balance by (1 + rate) each period, so the base keeps increasing.

With $5,000 at 6% for one year, both give $300. The formulas only diverge from year two onward — which is why short-term comparisons hide the real story.

Plotted over time, simple interest is a straight ramp and compound interest is a curve that bends upward. For the first few years the lines nearly overlap — compounding looks unimpressive up close.

The curve’s late acceleration is the whole point: in the example above, compound growth earns more in years 21–30 ($12,682) than simple interest earns across all 30 years combined ($9,000). Patience is literally where the money is.

You will meet simple interest mainly in short-term lending: some auto loans, short-term personal loans, and certain bonds compute interest on the original principal. It is predictable and easy to audit.

Compound interest dominates savings accounts, certificates of deposit, money-market accounts, and investment growth — and, less pleasantly, credit-card balances and unpaid loan interest that capitalizes. Compounding works for whoever receives the interest, so it rewards savers and punishes borrowers equally.

• Usually simple: some auto/personal loans, US savings bonds (electronic), short-term notes.
• Usually compound: savings accounts, CDs, investments, credit cards, capitalized student-loan interest.
• Always ask: “Does unpaid interest itself accrue interest, and how often does it compound?”

A 24% APR credit card compounds daily. On a $3,000 balance with no payments, daily compounding adds roughly $60 in the first month — and then charges interest on that $60 the next month. Minimum payments mostly feed the interest while the principal shrinks slowly.

This asymmetry is the most practical lesson of this guide: compound growth builds wealth on the saving side and destroys it on the borrowing side. Paying down high-rate debt is mathematically equivalent to earning that rate risk-free.

The annual percentage rate (APR) typically ignores compounding within the year, while the annual percentage yield (APY) includes it. A 6% APR compounded monthly is a 6.17% APY — the APY is the number that reflects what actually happens.

When comparing savings accounts, compare APY to APY. When comparing loans, compare APR to APR and ask about compounding and fees separately. Mixing the two measures is a classic way to misjudge a deal.