NumberTally Compound Interest Formula Explained
By NumberTally Tools · Updated October 2026 · 7 min read
Compound interest is interest earned on both your original money and the interest already added — the "snowball effect" that makes long-term saving so powerful. A small difference in rate or time can mean tens of thousands of dollars.
Here is the formula, what each piece means, and a worked example you can follow along with.
The compound interest formula
- A = final amount
- P = principal (starting amount)
- r = annual interest rate (as a decimal)
- n = times interest compounds per year
- t = years
Worked example: $10,000 at 7% for 20 years
Monthly compounding (n = 12):
- r/n = 0.07 ÷ 12 = 0.005833
- nt = 12 × 20 = 240
- A = 10,000 × (1.005833)²⁴⁰ ≈ 10,000 × 4.0387 = $40,387
Worked example
Your $10,000 quadrupled — and $30,387 of that is pure interest. Starting 10 years earlier beats saving twice as much later: time matters more than amount.
The Rule of 72 shortcut
Want a quick estimate without the full formula? Divide 72 by your annual rate to get the years needed to double your money:
At 7%, money doubles roughly every 10.3 years. At 4%, every 18 years. That gap is why fees and low-yield accounts cost more than they appear to.
See your money grow:
Frequently asked questions
What is the compound interest formula?
A = P(1 + r/n)^(nt): final amount equals principal times one plus the periodic rate, raised to the total number of compounding periods.
What is the Rule of 72?
A shortcut: divide 72 by the annual interest rate to estimate how many years it takes money to double. At 8%, about 9 years.
How often should interest compound?
More frequent compounding (monthly vs yearly) grows money slightly faster, but the rate and the time invested matter far more than the compounding frequency.