Compound vs Simple Interest
Side-by-side formulas, numeric comparisons, and when each type applies to savings, loans, and investments.
9 min read · Last updated: July 13, 2026
Simple interest
Simple interest is calculated only on the original principal. Formula: I = P × r × t, where P is principal, r is annual rate (decimal), and t is time in years. Future value = P + I = P(1 + rt). Example: $10,000 at 5% for 10 years → I = 10,000 × 0.05 × 10 = $5,000 interest. Total = $15,000. Growth is linear — each year adds the same dollar amount ($500 here). Short-term bonds, some certificate structures, and certain personal loans quote simple interest because the balance does not accumulate earned interest as a new base for the next period.
Compound interest
Compound interest is calculated on principal plus all previously earned interest. Formula: A = P(1 + r/n)^(nt), where n is compounding periods per year. Same $10,000 at 5% compounded annually for 10 years: A = 10,000 × (1.05)^10 ≈ $16,288.95 — about $1,289 more than simple interest. With monthly compounding (n = 12): A ≈ $16,470. Growth is exponential; the gap widens every year. Daily compounding (n = 365) adds a small amount over monthly on the same nominal rate. The effective annual rate is always equal to or higher than the stated rate when compounding is more frequent than once per year.
10-year comparison at 5%
Starting $10,000, 5% annual rate, 10-year horizon. Simple interest total: $15,000 ($500/year). Annual compound: $16,289. Monthly compound: $16,470. At 20 years, simple = $20,000 vs annual compound ≈ $26,533 — a $6,533 gap from the same starting terms. At 7% over 30 years on $10,000: simple = $31,000; compound ≈ $76,123. Time and rate amplify the difference. Year-by-year, compound interest in year 10 earns $814 on the accumulated balance; simple interest still earns exactly $500. That acceleration is why long investment horizons favor accounts that reinvest returns.
Where each shows up
Most mortgages and auto loans use amortized compound-style math — you pay interest on the declining balance each month, not simple interest on the full original principal for the whole term. Some short-term consumer loans quote simple interest on the initial balance; read the disclosure. Savings accounts, CDs, and investment returns compound when earnings stay invested. Inflation erodes purchasing power at a compound-like effect over time — 3% annual inflation cuts $10,000 of buying power to roughly $7,441 in 10 years (10,000 × 0.97^10). Nominal account growth must exceed inflation to increase real wealth.
Adding regular deposits
Compound interest with monthly contributions accelerates growth further. $200/month added to $10,000 at 6% for 20 years grows to roughly $108,000 — far more than principal plus simple interest on deposits alone. Each contribution has less time to compound, but the steady inflow dominates long horizons. Retirement accounts and index funds rely on this combination. The Rule of 72 estimates doubling time: 72 ÷ rate ≈ years to double. At 6%, money doubles about every 12 years. Contributions shorten the path to each doubling because the base keeps growing.
Which model to use when planning
Use simple interest when the product explicitly states it — some promissory notes and short bridges. Use compound interest for savings projections, investment return estimates, and any scenario where earnings reinvest. For loans, use amortization (compound on the remaining balance) rather than simple interest on the full principal unless the contract says otherwise. When comparing offers, convert both to the same compounding frequency or compare APR/effective annual rate so you are not mixing incompatible assumptions.
Model both on CalcVo
The CalcVo Compound Interest Calculator projects savings with custom rates, compounding frequency, and contributions. The Loan Calculator shows amortized repayment. Use Investment Return and Savings Goal Calculators for planning targets, the Retirement Savings Calculator for long horizons, and the Inflation Calculator to see how today's dollars translate to future purchasing power. Adjust every input and watch results update instantly — compare simple vs compound paths side by side with your own numbers.