How to calculate compound interest: formula and examples

With compound interest, each period's interest is calculated on the initial principal plus all the interest accumulated so far. With simple interest, it is always calculated on the initial principal only. That's why, at the same rate and term, compound interest produces a larger result, and the gap widens over the years.

A = P × (1 + r/n)^(n·t)

• A: final amount.
• P: initial principal.
• r: nominal annual interest rate as a decimal (5% = 0.05).
• n: compounding periods per year (12 if monthly).
• t: number of years.

The fraction r/n is the interest rate per period, and the exponent n·t is the total number of periods.

Say you invest €10,000 at a 5% nominal annual rate, compounded monthly, for 10 years.

1. Rate per period: 0.05 / 12 ≈ 0.004167.
2. Number of periods: 12 × 10 = 120.
3. Growth factor: (1 + 0.05/12)^120 ≈ 1.6470.
4. Final amount: 10,000 × 1.6470 ≈ €16,470.09.

Of that final amount, €6,470.09 is interest. This is an illustrative example: it excludes taxes, fees and inflation.

At the same 5% nominal rate, compounding once a year instead of monthly leaves the example's final amount at €16,288.95: €181.14 less. The more often interest compounds, the sooner it starts earning interest, although the difference is moderate.

If you also add money every period, each contribution starts earning interest from the day it's deposited. For example, adding €100 a month for 10 years at 5% compounded monthly, with no initial principal, gives €15,528.23 if you contribute at the end of each month and €15,592.93 if you contribute at the start, because each contribution compounds for one more month.

• Confusing the nominal rate with the annual percentage yield or APR, which already reflect compounding and, where relevant, fees.
• Forgetting taxes and fees, which reduce the final return.
• Ignoring inflation: a larger balance doesn't always mean more purchasing power.
• Assuming a variable return will stay constant for the whole term.