How to Calculate Compound Interest (With Contributions)
Compound interest means you earn returns on prior returns. The growth curve bends upward over long horizons—**time** and **contribution consistency** usually matter more than small rate tweaks in the first decade.
Core formula
A = P(1 + r/n)^(nt) · contributions add per periodStep by step
1. Define P, r, n, t
P = starting principal, r = annual nominal rate (decimal), t = years, n = compounding periods per year (12 monthly, 365 daily, etc.).
2. Apply A = P(1 + r/n)^(nt)
For monthly compounding of annual rate 6%: use r/n = 0.06/12 per month and nt = 12×t.
3. Add periodic contributions
Future value with contributions is easiest in a calculator—each deposit compounds for remaining periods.
Compounding frequency comparison
More frequent compounding slightly increases effective yield at the same nominal rate.
- Annual: Simplest; understates growth vs monthly for savings products.
- Monthly: Common for savings accounts and many models.
- Daily: Slightly higher effective APY than monthly at same nominal rate.
- Nominal vs APY: APY reflects compounding; use APY to compare bank products.
Use our calculators
Common mistakes
- Using annual rate without dividing by periods
- Forgetting contributions in long-term plans
- Comparing nominal rate to APY directly
FAQ
Rule of 72?
Years to double ≈ 72 ÷ interest rate (percent)—handy estimate for mental math.
Does inflation matter?
Yes—subtract an inflation assumption for “real” purchasing power.