How to Calculate Compound Interest

The compound interest formula

Simple interest pays only on your original capital. Compound interest also pays on the interest already earned, which is why balances accelerate over time.

• A = P (1 + r/n)^(n × t)
• P = starting amount, r = annual rate as a decimal, n = compounding periods per year, t = years
• Example: 10,000 at 7% compounded monthly for 20 years → 10,000 × (1 + 0.07/12)^240 ≈ 40,400

Why the compounding frequency matters

More frequent compounding helps, but with diminishing returns: the gap between daily and monthly compounding is small compared with the gap between annual and monthly.

Adding regular contributions

Most people do not invest a lump sum — they add money every month. The future value of a regular contribution is calculated with a second term.

• FV = P(1 + r/n)^(nt) + C × ((1 + r/n)^(nt) − 1) ÷ (r/n)
• C is the contribution made each compounding period.
• Example: 10,000 plus 250 a month at 7% for 20 years grows to roughly 170,000, of which about 100,000 is interest.

In that example your contributions total 70,000 and interest adds 100,000. After about a decade, the interest earned each year exceeds the amount you contribute — that is compounding doing the work.

The rule of 72

A quick way to estimate doubling time: divide 72 by the annual percentage rate. At 7%, money doubles in roughly 10.3 years; at 3%, in about 24 years.

It is an approximation, but accurate enough for back-of-an-envelope planning.

What the formula does not include

• Inflation — subtract it from your rate to see real growth.
• Fees and tax — a 1% annual fee can remove a quarter of a long-term balance.
• Volatility — real returns vary; compounding assumes a smooth path.