Compound Interest Calculator
Calculate compound interest growth using A = P(1+r/n)^(nt).
Compare daily, monthly, and annual compounding and see how time and rate affect final balance.
Compound interest is the process of earning interest on both your original principal and on previously accumulated interest — “interest on interest” — creating exponential rather than linear growth.
Core formula: A = P × (1 + r/n)^(n×t)
Where:
- A = final amount (principal + total interest earned)
- P = principal (initial deposit or investment)
- r = annual interest rate as a decimal (e.g., 7% = 0.07)
- n = number of compounding periods per year (1=annual, 12=monthly, 365=daily)
- t = time in years
- Interest Earned = A − P
Continuous compounding (theoretical maximum): A = P × e^(r×t)
Effect of compounding frequency on $10,000 at 6% for 10 years:
| Compounding | Final Amount | Interest Earned |
|---|---|---|
| Annual (n=1) | $17,908 | $7,908 |
| Quarterly (n=4) | $18,061 | $8,061 |
| Monthly (n=12) | $18,194 | $8,194 |
| Daily (n=365) | $18,221 | $8,221 |
| Continuous | $18,221 | $8,221 |
Worked example: You invest $5,000 at 7% annual interest, compounded monthly, for 25 years. A = $5,000 × (1 + 0.07/12)^(12×25) A = $5,000 × (1.005833)^300 A = $5,000 × 5.4274 = $27,137 Interest earned = $27,137 − $5,000 = $22,137 — more than 4× your original investment
The Rule of 72: Divide 72 by the annual interest rate to estimate how long it takes to double your money. At 6%: 72 ÷ 6 = 12 years to double At 9%: 72 ÷ 9 = 8 years to double
Einstein allegedly called compound interest “the eighth wonder of the world.” Whether true or not, the math is undeniable: time is the most powerful variable. Starting 10 years earlier often matters more than contributing twice as much.