Compound interest calculator
Work out how an investment grows under compound interest, including regular contributions, the effect of inflation, and a year-by-year breakdown.
What is compound interest?
Compound interest is the process where credited interest is added to the principal and then earns interest alongside it in the next period. You earn interest on interest, and the money starts working on itself.
At the end of each compounding period, interest calculated on the current value is added to the balance, which raises the base for the next calculation. The more often interest is credited and the longer the horizon, the stronger the effect: the growth is exponential rather than linear.
The difference from simple interest is fundamental. With simple interest the interest is always calculated on the original amount, so it grows evenly. With compound interest the base grows with every period, which is why the growth curve keeps accelerating. That is exactly why time is the most important variable, not the size of the contribution.
The formula and where it comes from
The calculation has two independent parts that are added together at the end. The first compounds the one-off initial investment, the second handles the regular contributions.
Each period the balance is multiplied by the factor (1 + r/n). After n·t periods that factor has applied exactly that many times: hence the exponent. The exponent is the mathematical statement that interest is calculated on an amount that has already earned interest.
Each individual contribution earns interest for a different length of time: the first for the whole period, the last barely at all. Rather than summing hundreds of individual terms, the closed form of a geometric series gives the same answer in a single calculation.
What each variable means
Getting the units right is essential. The most common mistake comes from exactly this: confusing a percentage with a decimal, or an annual rate with a per-period one.
| Symbol | Name | Jednotka |
|---|---|---|
| Future value | € | |
| Initial investment | € | |
| Annual interest rate | ||
| Compounding periods per year | ||
| Investment period | years | |
| Rate per period | ||
| Total number of periods | ||
| Contribution per period | € |
A worked example
Common mistakes
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Related terms
Every term used in this calculator has its own encyclopedia entry with a detailed explanation and derivation.
Related topics
Terms that come up in this calculation
- Compound interestA way of charging interest in which the interest credited is added to the principal and earns alongside it in the next period, so you earn on interest earned earlier too.
- Effective interest rateThe true annual return once the frequency of compounding is accounted for. It lets you compare two offers fairly when they show the same figure on paper.
- InflationThe general rise in prices across an economy, which gradually erodes the purchasing power of money: the same sum buys less in a few years than it does today.
- Present value (PV)What a future sum of money is worth today. It answers the question "how much would I have to have now for it to grow into that".
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- FIREFind out when you reach financial independence, with your FIRE number, a year-by-year portfolio projection, the passive income and scenarios side by side.