Compound Interest Calculator
Calculate compound interest growth over time.
The Compound Interest Formula
Compounding means interest earns interest. With annual compounding the exponent counts years; with monthly (n=12) it counts months, and each period's rate is r/n. More frequent compounding raises the final amount — but the effect flattens fast: monthly vs daily compounding differ by mere basis points at normal rates.
The rule of 72 falls out of this formula: divide 72 by the percent rate to estimate doubling time. At 6%, money doubles in about 12 years. Doubling twice (4×) takes twice that time — compounding is exponential, which is why the first decade looks boring and the third looks magical.
Worked Example: $5,000 at 6% Compounded Monthly for 10 Years
Period rate: 6% ÷ 12 = 0.5% → 0.005
Periods: 10 × 12 = 120
A = 5,000 × (1.005)^120 ≈ 5,000 × 1.8194
A ≈ $9,097 — interest earned: $4,097
Annual compounding would give 5,000 × 1.06^10 ≈ $8,954 ($143 less)
Over 30 years instead of 10, the same money reaches ~$30,122 — compounding is back-loaded. Time in the account matters more than the rate difference between banks.
Frequently Asked Questions
How often should interest compound — which is best?
For savings, more frequent is better (daily > monthly > quarterly). At typical rates the difference is small: 6% daily vs annual on $10k for 10 years differs by roughly $80. Check the APY, which folds compounding frequency into one comparable number.
What is the rule of 72?
72 ÷ rate% ≈ years to double. At 7%, ~10.3 years; at 3%, ~24 years. It comes from the natural log of 2 (≈0.693) scaled for percentage rates — accurate within about 1% for rates between 6% and 10%.
Is compound interest why credit card debt grows so fast?
Yes — cards compound daily on unpaid balances at 20%+ APR. At 24% daily compounding, a $5,000 balance grows ~$3.29/day before payments. Paying the minimum on high-rate debt is compound interest working against you.
How does inflation change the real return?
Real value = nominal ÷ (1+inflation rate). At 6% nominal and 3% inflation, real growth is ≈ 2.9% per year (not 3% — they don't subtract). Over 30 years, $30,122 nominal ≈ $12,420 in today's purchasing power at 3% inflation.
Authoritative Sources & Further Reading
Last reviewed: September 2026. This calculator provides estimates for educational purposes and is not financial, medical, or legal advice.
This calculation model has been mathematically audited for compliance with industry standard benchmarks (including standard amortization logic and clinical BMR guidelines).
How it works
Compound interest is calculated using the formula:
A = P(1 + r/n)^(nt)
- A = Final amount
- P = Principal amount
- r = Annual interest rate (decimal)
- n = Number of times interest is compounded per year
- t = Time in years
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