Compound Interest Formula
Calculate compound interest with A = P(1+r/n)^nt.
See how principal, rate, and compounding frequency grow your money over time.
The Formula
Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods. This is what makes savings grow exponentially over time.
Variables
| Symbol | Meaning |
|---|---|
| A | Final amount (principal + interest) |
| P | Principal (initial investment or loan amount) |
| r | Annual interest rate (as a decimal, e.g. 5% = 0.05) |
| n | Number of times interest is compounded per year |
| t | Time in years |
Compounding Frequencies
| Frequency | n value |
|---|---|
| Annually | 1 |
| Semi-annually | 2 |
| Quarterly | 4 |
| Monthly | 12 |
| Daily | 365 |
| Continuously | A = P × e^(r×t) |
Example 1
You invest $10,000 at 6% annual interest, compounded monthly, for 5 years. What is the final amount?
P = $10,000, r = 0.06, n = 12, t = 5
A = 10,000 × (1 + 0.06/12)^(12×5)
A = 10,000 × (1.005)^60
A = 10,000 × 1.34885
A = $13,488.50 (you earned $3,488.50 in interest)
Example 2
How much do you need to invest today at 8% compounded annually to have $50,000 in 10 years?
Rearrange: P = A / (1 + r/n)^(n×t)
P = 50,000 / (1 + 0.08)^10
P = 50,000 / 2.15892
P = $23,159.67 (invest this amount today)
When to Use It
Use the compound interest formula for financial planning:
- Projecting savings account or investment growth over time
- Comparing different compounding frequencies (monthly vs. annually)
- Calculating the total cost of a loan with compound interest
- Planning retirement savings goals