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⚠️ Disclaimer: This calculator provides estimates for educational purposes. Actual returns depend on rate fluctuations, taxes, fees, and other factors. Consult a financial advisor for investment decisions.
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Sources & Methodology
Compound interest formula verified against Investopedia financial reference library and Corporate Finance Institute (CFI) standards.
Investopedia — Compound Interest
Standard compound interest formula, compounding frequency definitions, and effective annual rate methodology
Corporate Finance Institute — Compound Interest
Compounding frequency tables and effective annual rate conversion formula used in this calculator
Formula: A = P × (1 + r/n)^(n×t). Where A = future value, P = principal, r = annual rate (decimal), n = compounding periods per year, t = years. Total Interest: A − P. Effective Annual Rate (EAR): (1 + r/n)^n − 1. Year-by-year table shows balance at end of each year.
⏱ Last reviewed: April 2026
How Periodic Compound Interest Is Calculated
Compound interest is the process where interest earned is added back to the principal so that future interest is calculated on an ever-growing base. Unlike simple interest (which only calculates interest on the original principal), compound interest accelerates growth exponentially over time. The compounding frequency — how often interest is applied — directly impacts the final amount.
The Compound Interest Formula
A = P × (1 + r/n)^(n × t)
P = $10,000 | r = 6% (0.06) | n = 12 (monthly) | t = 10 years
A = 10,000 × (1 + 0.06/12)^(12×10) = 10,000 × (1.005)^120 = $18,193.97
Total interest earned: $18,193.97 − $10,000 = $8,193.97
A = 10,000 × (1 + 0.06/12)^(12×10) = 10,000 × (1.005)^120 = $18,193.97
Total interest earned: $18,193.97 − $10,000 = $8,193.97
Impact of Compounding Frequency at 6% for 10 Years on $10,000
| Compounding | Periods/Year | Future Value | Total Interest | EAR |
|---|---|---|---|---|
| Annual | 1 | $17,908.48 | $7,908.48 | 6.000% |
| Semi-Annual | 2 | $18,061.11 | $8,061.11 | 6.090% |
| Quarterly | 4 | $18,140.18 | $8,140.18 | 6.136% |
| Monthly | 12 | $18,193.97 | $8,193.97 | 6.168% |
| Daily | 365 | $18,219.44 | $8,219.44 | 6.183% |
The Rule of 72 — How Long to Double Your Money
The Rule of 72 provides a quick estimate: Years to double = 72 / annual interest rate. At 6%, money doubles in approximately 12 years. At 9%, about 8 years. At 12%, about 6 years. The exact formula is t = ln(2) / ln(1 + r) = 0.693147 / ln(1.06) = 11.9 years at 6%. The Rule of 72 is accurate to within 1-2% for typical interest rates.
Effective Annual Rate (EAR)
The Effective Annual Rate converts a nominal rate with periodic compounding into the equivalent single annual rate. EAR = (1 + r/n)^n − 1. For 6% compounded monthly: EAR = (1 + 0.005)^12 − 1 = 6.168%. This means monthly compounding at 6% nominal is equivalent to 6.168% compounded annually. Always compare investments using EAR, not nominal rates.
💡 Power of Time: At 7% compounded monthly, $10,000 grows to $20,097 after 10 years, $40,388 after 20 years, and $81,164 after 30 years. The third decade adds more than the first two combined. Starting early is far more valuable than investing a larger amount later.
Frequently Asked Questions
A = P × (1 + r/n)^(n×t). A = future value, P = principal, r = annual interest rate (decimal), n = compounding periods per year, t = time in years. For $10,000 at 6% compounded monthly for 5 years: A = 10,000 × (1 + 0.005)^60 = $13,488.50.
Daily compounding (n=365) applies interest every day; monthly (n=12) applies it once per month. Daily compounding earns slightly more because each day's interest begins compounding sooner. On $10,000 at 6% for 10 years: daily gives $18,219 vs monthly's $18,194 — a difference of about $25.
More frequent compounding increases effective returns. For 6% nominal: annual EAR = 6.00%, semi-annual = 6.09%, quarterly = 6.14%, monthly = 6.17%, daily = 6.18%. The difference grows with higher rates and longer time horizons. At typical savings rates, the effect is small — securing a higher nominal rate matters far more than compounding frequency.
EAR = (1 + r/n)^n − 1. It converts a nominal rate with periodic compounding to an equivalent single annual rate. For 6% nominal compounded monthly: EAR = (1.005)^12 − 1 = 6.168%. EAR enables fair comparison between investments with different compounding frequencies — always compare using EAR, not stated nominal rates.
Use the Rule of 72: Years to double = 72 / annual rate. At 6%, about 12 years. At 8%, about 9 years. At 12%, about 6 years. Exact: t = ln(2) / ln(1+r). For 6%: 0.693 / ln(1.06) = 11.9 years. The Rule of 72 is accurate within 1-2% for rates between 6-12%.
Continuous compounding is the theoretical limit where interest is applied infinitely frequently. Formula: A = P × e^(r×t). For $10,000 at 6% for 10 years: A = 10,000 × e^0.6 = $18,221.19. This exceeds daily compounding ($18,194) by only $27 — the practical difference between daily and continuous is negligible.
More frequent compounding is always better for savers. Daily beats monthly, monthly beats quarterly, quarterly beats annual. In practice, the differences are small at typical savings rates (0-5%). A bank offering 4.5% with daily compounding is better than one offering 4.4% with monthly compounding, but a 4.5% daily rate is far better than a 3% daily rate.
Use t as a decimal in A = P(1+r/n)^(n×t). For 18 months (1.5 years) at 6% monthly compounding: A = P × (1.005)^18. Enter 1.5 in the years field. For 3 months (0.25 years): A = P × (1.005)^3. The formula handles any fractional time period naturally.
The nominal rate is the stated annual rate (e.g., 6%). The effective rate (EAR) accounts for compounding and shows the true annual yield. For 6% nominal: monthly compounding gives EAR of 6.168%, daily gives 6.183%. A credit card stating 24% APR compounded monthly has an EAR of 26.82% — the effective rate is what borrowers actually pay.
Simple interest: I = P × r × t (interest only on original principal). Compound interest applies interest on both principal and accumulated interest. For $10,000 at 6% over 10 years: simple interest gives $16,000 (constant $600/year); compound interest (monthly) gives $18,194. The gap widens significantly over longer time periods.
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