Compound Interest Formula
Calculate compound interest with the formula A = P(1 + r/n)^(nt).
Learn how your money grows over time with interest compounding.
The Formula
Compound interest is interest earned on both the original principal and on previously accumulated interest. This is what makes savings grow faster over time compared to simple interest.
Variables
| Symbol | Meaning |
|---|---|
| A | Final amount (principal + interest) |
| P | Principal (initial investment or deposit) |
| r | Annual interest rate (as a decimal, so 5% = 0.05) |
| n | Number of times interest compounds per year |
| t | Number of years |
Example 1
You invest $5,000 at 6% annual interest, compounded monthly, for 10 years.
P = $5,000, r = 0.06, n = 12, t = 10
A = 5000 × (1 + 0.06/12)^(12 × 10)
A = 5000 × (1 + 0.005)^(120)
A = 5000 × (1.005)^120
A = 5000 × 1.8194
A = $9,097.00 — You earned $4,097 in interest.
Example 2
You deposit $10,000 at 4% annual interest, compounded quarterly, for 5 years.
P = $10,000, r = 0.04, n = 4, t = 5
A = 10000 × (1 + 0.04/4)^(4 × 5)
A = 10000 × (1 + 0.01)^(20)
A = 10000 × (1.01)^20
A = 10000 × 1.2202
A = $12,202.00 — You earned $2,202 in interest.
When to Use It
Use the compound interest formula when:
- You want to know how much a savings account or investment will grow over time
- You need to compare different compounding frequencies (monthly vs. quarterly vs. annually)
- You are planning for retirement, college funds, or long-term savings goals
- You want to understand the true cost of a loan that compounds interest
Key Notes
- Formula: A = P(1 + r/n)^(nt): P is principal, r is annual nominal rate, n is compounding periods per year, t is years. More frequent compounding (larger n) gives higher returns but with rapidly diminishing gains — the difference between daily and monthly compounding is usually under 0.1%.
- Compound vs simple interest: Simple interest: A = P(1 + rt) grows linearly. Compound interest grows exponentially. Over 30 years at 8%, $10,000 becomes $100,627 with annual compounding vs $34,000 with simple interest — compound interest delivers nearly 3× more.
- Continuous compounding: A = Pe^(rt): The theoretical maximum for a given nominal rate. For r = 8%, continuous APY = e^0.08 − 1 ≈ 8.329% vs 8.0% annual compounding. The mathematics is cleaner and it is used in financial derivatives pricing (Black-Scholes).
- Tax drag on compound growth: Taxes paid on annual interest income break the compounding cycle. $10,000 at 8% for 30 years: tax-deferred grows to $100,627; taxed annually at 25% effectively yields ~6% net, growing to only $57,435. Tax-advantaged accounts (401k, IRA, ISA) preserve the full compounding effect.
- Applications: Compound interest calculations underlie savings account projections, mortgage balance growth, student loan capitalization, inflation-adjusted value projections, and the time-value-of-money principle that is the foundation of all of corporate finance.