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