Compound Interest vs Simple Interest
Simple interest and compound interest both calculate the cost of borrowing or the return on lending, but they diverge significantly over time. Simple interest applies only to the original principal. Compound interest applies to the growing balance — interest earns interest, creating exponential growth.
In practice: most savings accounts, investment accounts, and mortgages use compound interest. Simple interest applies to short-term loans, some personal loans, and US Treasury bonds. Knowing which type applies to your financial product determines how much you actually earn or owe.
The Formulas Side by Side
Simple Interest: Interest = P × r × t Final amount = P × (1 + r × t) Compound Interest (compounded annually): Final amount = P × (1 + r)^t Example: $10,000 at 5% for 10 years Simple: 10,000 × (1 + 0.05 × 10) = $15,000 Compound: 10,000 × (1.05)^10 = $16,289 Difference: $1,289 — all from interest earning interest
Growth Comparison Over Time
$10,000 at 6% annual rate: Year Simple ($) Compound ($) Difference ($) ──── ────────── ──────────── ────────────── 1 10,600 10,600 0 5 13,000 13,382 382 10 16,000 17,908 1,908 20 22,000 32,071 10,071 30 28,000 57,435 29,435 40 34,000 102,857 68,857
When Simple Interest Is Used
Simple interest is used for short-term loans where the interest does not roll over into the principal. Car loans in many countries use simple interest — the interest is calculated on the original loan amount, not the growing balance. Some personal loans, pawn shop loans, and US Treasury bills (T-bills) also use simple interest.
For short periods, simple and compound interest produce nearly identical results. At 5% for 1 year, simple gives $500 interest on $10,000; compound gives $500 as well (the difference only emerges when interest accumulates over multiple periods).
When Compound Interest Is Used
Compound interest is used in savings accounts, certificates of deposit, mortgages, credit cards, and most investment vehicles. In savings accounts, compounding typically happens daily or monthly. In mortgages, payments are structured so that early payments are mostly interest, shifting toward principal over time (amortization).
Credit cards compound daily in most US products. On a $3,000 balance at 24% APR, monthly minimum payments extend payoff to many years and total interest often exceeds the original balance.
Quick Tips
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For savings: always prefer compound interest. The higher the compounding frequency (daily vs monthly vs annual), the more you earn.
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For debt: understand that your credit card balance compounds. Paying in full each month avoids compound interest entirely.
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Ask your bank: 'Does this account compound daily or monthly?' Daily compounding earns slightly more.
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The Rule of 72 only applies to compound interest. For simple interest, doubling time = 100 ÷ rate years.
Frequently Asked Questions
Is a mortgage simple or compound interest?
Mortgages use compound interest but are structured as amortizing loans — fixed monthly payments that gradually shift from mostly interest to mostly principal. The balance accrues interest on the outstanding principal each month.
Why does compound interest grow faster?
Because each period's interest is added to the principal, making the base for the next period's calculation larger. This feedback loop accelerates growth exponentially over time.
Does simple interest ever make more sense?
For short-term situations (under 1 year), simple and compound interest give nearly the same result. Simple interest loans can be simpler to calculate manually and to pay off, since the outstanding balance does not surprise you.
How do I know which type applies to my loan or account?
Read the terms. Look for 'compound interest,' 'compounded daily/monthly,' or 'amortized' (which implies compound). Simple interest loans usually say so explicitly. When in doubt, ask the lender directly.
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