The Compound Interest Formula
The standard formula for compound interest is:
A = P(1 + r/n)nt
Where:
- A = Final amount (principal + interest)
- P = Principal (initial investment)
- r = Annual interest rate (decimal form)
- n = Number of times interest compounds per year
- t = Time in years
Step-by-Step Example
Let's calculate the final balance for a $5,000 investment at 6% annual interest, compounded monthly, over 10 years.
Step 1: Identify variables
- P = $5,000
- r = 0.06 (6% as decimal)
- n = 12 (monthly compounding)
- t = 10 years
Step 2: Apply the formula
A = 5000 × (1 + 0.06/12)12×10
A = 5000 × (1.005)120
A = 5000 × 1.8194
A ≈ $9,096.98
What About Continuous Compounding?
In theoretical finance, continuous compounding uses the formula:
A = Pert
Where e is Euler's number (≈ 2.718). Continuous compounding represents the theoretical maximum growth for a given rate and time.
How Compounding Frequency Affects Growth
More frequent compounding means faster growth. For the same $5,000 at 6% over 10 years:
- Annually (n=1): ≈ $8,954
- Quarterly (n=4): ≈ $9,070
- Monthly (n=12): ≈ $9,097
- Daily (n=365): ≈ $9,110
Using a Calculator
While the formula is straightforward, manually computing large exponents can be tedious. Our compound interest calculator handles all the math instantly — just input your principal, rate, time, and compounding frequency to see your results.
Conclusion
The compound interest formula is a fundamental tool in personal finance and investing. Mastering it helps you evaluate savings accounts, investment returns, and loan costs with confidence.