Simple Interest vs. Compound Interest
Simple interest calculates interest only on the original principal. If you invest $1,000 at 10% simple interest for 5 years, you earn $100/year = $500 total profit.
Compound interest calculates interest on your principal and on previously earned interest. The interest is reinvested, creating exponential growth rather than linear growth. The same $1,000 at 10% compounded annually for 5 years yields $610.51 — 22% more.
The Compound Interest Formula
Where each variable means:
- A — Final amount (principal + total interest earned)
- P — Principal (the initial amount invested or borrowed)
- r — Annual interest rate expressed as a decimal (e.g., 7% = 0.07)
- n — Number of times interest is compounded per year
- t — Time in years
Step-by-Step Worked Example
You invest $5,000 at an annual interest rate of 7%, compounded monthly (n = 12) for 10 years.
- Convert rate to decimal: r = 0.07
- Plug into formula: A = 5000 × (1 + 0.07/12) ^ (12 × 10)
- A = 5000 × (1.005833) ^ 120
- A = 5000 × 2.0097
- A = $10,048.50
Your $5,000 more than doubled in 10 years, and you earned $5,048.50 in pure interest — without adding another cent.
How Compounding Frequency Changes Everything
Using $10,000 at 6% annual rate over 10 years, here's how frequency affects the final amount:
| Frequency | n value | Final Amount |
|---|---|---|
| Annually | 1 | $17,908 |
| Quarterly | 4 | $18,061 |
| Monthly | 12 | $18,194 |
| Daily | 365 | $18,220 |
The Rule of 72
The Rule of 72 is a quick mental shortcut to estimate how many years it takes to double your investment: divide 72 by the annual interest rate.
At 6% annual return: 72 ÷ 6 = 12 years to double. At 9%: 72 ÷ 9 = 8 years. This is a rough approximation but accurate to within 1–2 years for rates between 2–30%.
Adding Monthly Contributions
Most real investment scenarios involve adding money regularly. If you contribute an extra amount C every compounding period, the formula extends to:
Our calculator handles this automatically — just enter a monthly contribution amount to see how dramatically it accelerates your growth.