How to Calculate Compound Interest — Formula, Examples & Calculator

Knowing how to calculate compound interest is one of the most practical financial skills you can have. It lets you estimate how fast your savings grow, compare investment options, and spot when a lender is charging more than the headline rate suggests. This guide walks you through the formula, a full worked example, the Rule of 72, and what changes when you add monthly contributions.

Simple Interest vs. Compound Interest

Before running any numbers, it helps to understand what makes compound interest different from simple interest.

With simple interest, you earn a fixed amount every year based solely on your original principal. The interest never earns interest of its own.

With compound interest, each year's interest is added to the principal. The following year you earn interest on the enlarged balance — and so on, year after year.

Year	Simple interest (5% on €1,000)	Compound interest (5% on €1,000)
1	€1,050	€1,050
2	€1,100	€1,102.50
5	€1,250	€1,276.28
10	€1,500	€1,628.89
20	€2,000	€2,653.30
30	€2,500	€4,321.94

After 30 years the difference is dramatic: €2,500 with simple interest versus €4,322 with compounding — from the same €1,000 at the same 5% rate. The gap widens every year because compounding is exponential, not linear.

The Compound Interest Formula

The standard annual compound interest formula is:

A = P × (1 + r)^n

• A = final amount after n years
• P = principal (initial investment)
• r = annual interest rate as a decimal (e.g. 6% = 0.06)
• n = number of years

When interest compounds more frequently than once a year — monthly, for instance — the formula adjusts:

A = P × (1 + r/m)^(m×n)

Here m is the number of compounding periods per year. Monthly compounding means m = 12. More frequent compounding produces a slightly higher final amount because interest starts earning interest sooner within each year.

Step-by-Step Example: €5,000 Over 20 Years

Let's work through a realistic scenario. You deposit €5,000 at 7% annual interest and leave it untouched for 20 years.

Step 1: Identify your variables.
P = €5,000 · r = 0.07 · n = 20

Step 2: Calculate the growth factor.
(1 + 0.07)^20 = 1.07^20

To compute 1.07^20 without a calculator, use logarithms or an approximation. The exact value is 3.8697.

Step 3: Multiply by the principal.
A = 5,000 × 3.8697 = €19,348.42

Your €5,000 grew to just under €19,350 — nearly four times the original amount — without adding a single euro. The total interest earned is €14,348, all of it generated by the compounding effect.

Year	Balance	Interest earned that year
1	€5,350.00	€350.00
5	€7,012.76	€459.44
10	€9,835.76	€644.57
15	€13,795.16	€904.30
20	€19,348.42	€1,268.39

Notice that the interest earned in year 20 (€1,268) is 3.6 times larger than in year 1 (€350). You did nothing different — compounding did the work automatically.

The Rule of 72: Calculate Doubling Time in Your Head

The Rule of 72 is a mental shortcut to estimate how long it takes for an investment to double. Divide 72 by the annual interest rate:

Doubling time ≈ 72 ÷ interest rate (%)

At 6% per year, your money doubles in roughly 72 ÷ 6 = 12 years. At 9%, it doubles in 8 years. The rule is accurate enough for quick comparisons and requires no calculator at all.

Annual return	Rule of 72 (approx.)	Exact doubling time
2%	36.0 years	35.0 years
3%	24.0 years	23.4 years
5%	14.4 years	14.2 years
6%	12.0 years	11.9 years
7%	10.3 years	10.2 years
8%	9.0 years	9.0 years
10%	7.2 years	7.3 years
12%	6.0 years	6.1 years

The Rule of 72 also works in reverse: if inflation runs at 3% per year, purchasing power halves in roughly 24 years. Use the Rule of 72 calculator to explore any rate instantly, or the inflation calculator to see what rising prices do to your real returns.

Compound Interest With Monthly Contributions

A lump-sum investment is only part of the picture. Most people build wealth by investing a fixed amount every month — a savings plan. Regular contributions interact with compounding in a powerful way.

The formula for the future value of regular contributions is:

FV = PMT × [((1 + r/m)^(m×n) − 1) / (r/m)]

• PMT = monthly contribution
• r = annual interest rate as a decimal
• m = 12 (monthly compounding)
• n = years

If you also start with an initial lump sum P, add A = P × (1 + r/m)^(m×n) to the result above.

The longer the time horizon, the more dramatic the effect. In this example you contributed €60,000 and received €162,705 — the compounding effect more than doubled your own money.

Combine an initial deposit with regular contributions in the savings plan calculator to model your own scenario precisely.

Common Mistakes When Calculating Compound Interest

1. Ignoring inflation

A nominal return of 7% sounds great. But if inflation runs at 2.5%, your real return is closer to 4.5%. Over 20 years, the difference between nominal and real growth is enormous. Always subtract inflation from your expected return when planning long-term. The inflation calculator quantifies the exact impact.

2. Forgetting fees and costs

An annual fund management fee of 1.5% might look small. Against a 7% gross return it reduces your net return to 5.5% — and over 30 years that single percentage point costs you roughly 25% of your final balance. Always use the net-of-fees return in your calculations.

3. Not accounting for taxes

In many countries, investment gains are taxed annually or at withdrawal. A 25% capital gains tax on each year's interest reduces your effective compounding rate. For tax-advantaged accounts the difference is especially large over long periods.

4. Confusing nominal and effective annual rates

A savings account advertising "6% per year, compounded monthly" has an effective annual rate of (1 + 0.06/12)^12 − 1 = 6.17%, not 6%. The difference matters when comparing products that compound at different frequencies.

5. Withdrawing gains during the accumulation phase

Every withdrawal resets part of the compounding base. If you take out dividends or interest instead of reinvesting them, you switch compounding off. Accumulating ETFs or automatic reinvestment plans avoid this mistake entirely.

6. Underestimating the impact of starting late

Starting 10 years later does not mean 10 years less growth. At 7%, a 10-year delay roughly halves your final balance because you lose the most powerful phase of compounding — the final years when the balance is largest. The formula makes this concrete: every year removed from n is a year you don't multiply by 1.07.

Conclusion

Calculating compound interest is straightforward once you know the formula — and the intuition behind it is even more important than the arithmetic. Three variables drive everything: the rate, the time, and whether you reinvest your returns.

1. Use the formula A = P × (1 + r)^n for lump-sum calculations.
2. Apply the Rule of 72 for instant doubling-time estimates.
3. Add regular contributions to turbocharge the compounding effect.
4. Deduct inflation, fees, and taxes to get a realistic net return.
5. Start as early as possible. Time cannot be bought back.

For anything beyond back-of-envelope math, a calculator removes the risk of arithmetic errors and shows the full year-by-year picture instantly.

More useful calculators: Savings Plan Calculator · Rule of 72 Calculator · Inflation Calculator