Compound interest is the foundation of wealth building. This guide walks through the formula step by step so you can calculate compound interest by hand or verify what any calculator tells you.
Step 1: Identify Your Variables
The compound interest formula has four variables: P (principal or starting amount), r (annual interest rate as a decimal), n (number of times interest compounds per year), and t (time in years). Make sure to convert the percentage rate to a decimal by dividing by 100: 6% becomes 0.06.
Step 2: Apply the Formula
A = P(1 + r/n)^(n × t) A = final amount, P = principal, r = annual rate (decimal), n = compounds per year, t = years.
Worked Example
$10,000 invested at 6% annual interest, compounded monthly, for 10 years:
- P = 10,000, r = 0.06, n = 12, t = 10
- A = 10,000 × (1 + 0.06/12)^(12 × 10)
- A = 10,000 × (1.005)^120
- A = 10,000 × 1.8194 = $18,193.97
You earned $8,193.97 in interest on a $10,000 investment. Verify with the Compound Interest Calculator.
Step 3: Adding Monthly Contributions
Most investors add money regularly. The future value of an annuity formula handles this:
FV = PMT × [((1 + r/n)^(n×t) − 1) / (r/n)] Add this to the compound interest result above to get the total future value.
Adding $200/month to the example above: FV = 200 × [((1.005)^120 − 1) / 0.005] = 200 × 163.88 = $32,776. Total portfolio: $18,194 + $32,776 = $50,970. You contributed $34,000 total ($10,000 + $200×120) and earned $16,970 in compound interest.
Model any scenario with 5 solve modes and Monte Carlo simulation
Try the Compound Interest Calculator →Step 4: Understand Compounding Frequency
| Frequency | n | $10,000 at 6% for 10 years |
|---|---|---|
| Annually | 1 | $17,908 |
| Quarterly | 4 | $18,140 |
| Monthly | 12 | $18,194 |
| Daily | 365 | $18,220 |
Key Takeaways
- The formula is A = P(1+r/n)^(nt) for lump-sum investments.
- Add the annuity formula for regular contributions to get total future value.
- More frequent compounding produces slightly higher returns, but the effect diminishes beyond monthly.
- Time is the most powerful variable — doubling the time period more than doubles the interest earned.