Compound interest: how a balance grows when interest stays in the account

To estimate what savings might grow to, separate the money you put in from the interest it earns. Compound interest means leaving that interest in the account so it can earn interest too. The rate, the time available and any later deposits determine the result.

The examples below use fixed rates, with no withdrawals, tax or fees unless stated. They explain the calculation; they are not forecasts of investment returns or recommendations about where to put money.

Follow the first two years

Start with €10,000 earning 5% a year, credited annually. After the first year, €500 of interest takes the balance to €10,500. In year two, 5% is applied to €10,500, so the interest is €525 and the balance becomes €11,025.

With simple interest, each year’s interest would remain €500 because it would always be calculated on the original €10,000.

After	Simple interest: final balance	Annual compound interest: final balance
1 year	€10,500	€10,500
10 years	€15,000	€16,289
25 years	€22,500	€33,864
40 years	€30,000	€70,400

Balances are rounded to whole euros. In the 40-year example, the compound balance includes about €60,400 of interest; the simple-interest balance includes €20,000. Neither figure includes new deposits.

When you need the formula

For a lump sum at a constant nominal annual rate:

final balance = starting amount × (1 + annual rate / periods per year)^(periods per year × years)

Use the rate as a decimal: 5% is 0.05. Annual compounding means one period per year; monthly means twelve. For example, €10,000 for ten years with annual compounding is 10000 × 1.05^10, or €16,288.95.

This formula assumes interest remains in the balance. If it is paid out and spent, it cannot earn more interest in that account.

Compare rates on the same basis

At the same nominal 5% annual rate, more frequent compounding produces a slightly higher balance:

Compounding, over ten years	Final balance on €10,000
Annually	€16,288.95
Monthly	€16,470.09
Daily, using 365 periods per year	€16,486.65

Here, monthly rather than annual compounding adds about €181. Daily rather than monthly adds about €17. These differences depend on the rate and term; the table is not a reason to ignore frequency in every comparison.

An effective annual rate includes the effect of compounding. A nominal 5% rate compounded monthly is about 5.116% effective per year. If an account already quotes an effective annual yield, do not treat it as a nominal rate and compound it again.

Regular deposits have less time to earn

A deposit made at the end of the year has not earned a full year’s interest. That is why adding all future deposits to the starting balance overstates the result.

For example, start with €1,000, add €100 at each month-end, and use a nominal 5% annual rate compounded monthly. After twelve months the balance is about €2,279.05: €2,200 paid in and €79.05 interest. Moving deposits to the start of each month changes the answer.

The compound interest calculator shows the balance, contributions, interest and effective annual rate. Its current mixed-frequency calculation can miss interest or deposits when the two frequencies do not align, including monthly/weekly and daily/monthly combinations. Use matching monthly settings to reproduce the deposit example above; check other arrangements against the account’s own calculation.

The savings goal calculator can estimate a monthly deposit for a target or a time to reach it. It also assumes a steady rate rather than changing market returns.

A quick doubling check

The rule of 72 estimates doubling time by dividing 72 by the annual percentage rate. At 6%, that gives twelve years. Annual compounding at exactly 6% gives about 11.9 years, so it is a useful rough check here.

It is an approximation for positive, steady rates and a lump sum. It does not account for deposits, fees or taxes, and it does not make a promised return more credible.

Include costs before interpreting a long projection

Reducing a steady annual return from 5% to 4% changes the €10,000, 40-year balance from about €70,400 to €48,010. That illustrates a one-percentage-point reduction in return, not the exact treatment of every 1% fee: fee timing and the amount charged matter.

Debt can also accumulate interest on unpaid interest, but the treatment depends on the agreement. A repayment loan needs a payment-by-payment schedule because each payment reduces the balance. A savings curve alone does not describe that loan.

Last reviewed 2 October 2026.