Compound Interest Formula — How to Calculate It (With Examples)
What Is the Compound Interest Formula?
The compound interest formula calculates how money grows when earned interest is reinvested and also earns interest. The standard formula is:
A = P(1 + r/n)nt
Where:
- A = Final amount (principal + interest)
- P = Principal (initial investment)
- r = Annual interest rate (as a decimal, so 5% = 0.05)
- n = Number of times interest compounds per year
- t = Number of years
Step-by-Step Example
Let’s calculate the future value of $10,000 invested at 7% annual interest, compounded monthly, for 20 years:
- Identify variables: P = $10,000, r = 0.07, n = 12, t = 20
- Plug into formula: A = 10,000 × (1 + 0.07/12)^(12 × 20)
- Simplify: A = 10,000 × (1.005833)^240
- Calculate: A = 10,000 × 4.0387 = $40,387.39
Your $10,000 grew by over $30,000 — that’s the power of compounding.
→ Try this calculation in our calculator
Compounding Frequency Comparison
The more frequently interest compounds, the more you earn:
| Frequency | n value | $10,000 at 7% for 20 years |
|---|---|---|
| Annually | 1 | $38,696.84 |
| Quarterly | 4 | $39,795.68 |
| Monthly | 12 | $40,387.39 |
| Daily | 365 | $40,552.37 |
| Continuously | ∞ | $40,552.00 |
The difference between annual and daily compounding on $10,000 over 20 years is $1,855.53.
Continuous Compounding Formula
When compounding happens infinitely (continuously), the formula becomes:
A = Pert
Where e is Euler’s number (approximately 2.71828). This is the theoretical maximum growth rate for a given interest rate.
Compound Interest Formula With Regular Contributions
Most people don’t just invest once — they add money regularly. The formula with monthly contributions is:
A = P(1 + r/n)nt + PMT × [((1 + r/n)nt - 1) / (r/n)]
Where PMT is the regular contribution amount.
Example with contributions
$10,000 initial + $500/month at 7% compounded monthly for 20 years:
- Principal growth: $40,387.39
- Contribution growth: $260,463.65
- Total: $300,851.04
The $500/month contributions ($120,000 total deposited) grew to over $260,000 thanks to compound interest.
→ Calculate with your own contributions
Quick Reference: Common Scenarios
- $1,000 at 5% for 10 years (monthly): $1,647.01
- $5,000 at 6% for 15 years (monthly): $12,270.47
- $25,000 at 7% for 30 years (monthly): $203,594.21
- $100,000 at 4% for 20 years (daily): $222,534.55
Related Tools
- Compound Interest Calculator — Calculate instantly with charts
- Rule of 72 — Quick mental math for doubling time
- Simple vs Compound Interest — See the difference visually
Frequently Asked Questions
What is the compound interest formula? ▾
The compound interest formula is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the annual interest rate (as a decimal), n is the number of compounding periods per year, and t is the number of years.
What's the difference between simple and compound interest formulas? ▾
Simple interest uses A = P(1 + rt) which grows linearly. Compound interest uses A = P(1 + r/n)^(nt) which grows exponentially because earned interest also earns interest.
How do I calculate compound interest monthly? ▾
Set n = 12 in the formula. For example, $10,000 at 5% compounded monthly for 10 years: A = 10000(1 + 0.05/12)^(12×10) = $16,470.09.