Finance & Investments
8 min read
•Updated 2026-09-17
Compound Interest Formula: Annual, Monthly, and Daily Compounding Explained
Explore Albert Einstein’s "eighth wonder of the world"—how compounding yields exponential gains through interest earned on prior interest.
By AnyCalcHub Wealth Research
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1. The Universal Compound Interest Formula
Compound interest is the addition of interest to the principal sum of a deposit or loan. It is interest on top of interest, causing a deposit or debt to grow at an accelerating rate.
Mathematical Formula
A = P × (1 + r/n)^(n × t)
Step-by-Step Worked Example
Principal (P)₹100,000
Annual Rate (r)10% (0.10)
Compounds per Year (n)12 (Monthly)
Years (t)10
Step 1:Periodic rate: 0.10 ÷ 12 = 0.008333
Step 2:Total compounding periods: 12 × 10 = 120
Step 3:Growth factor: (1.008333)^120 = 2.70704
Step 4:Maturity amount: 100,000 × 2.70704 = ₹270,704
Final Result: Total Interest Earned: ₹170,704 on ₹100,000 principal
2. The Rule of 72 Quick Mental Math
To quickly estimate how many years it will take for your money to double at a fixed compound interest rate, divide 72 by the annual interest rate.
Mathematical Formula
Years to Double ≈ 72 / Annual Interest Rate (%)
Step-by-Step Worked Example
Interest Rate12%
Step 1:Divide 72 by 12: 72 ÷ 12 = 6 years
Final Result: Your investment doubles approximately every 6 years
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Frequently Asked Questions
Common questions and mathematical nuances for this calculation.
What is the Effective Annual Rate (EAR)?
The EAR is the actual annual interest rate earned or paid, accounting for the effects of compounding during the year: EAR = (1 + r/n)^n - 1.
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