Compound Interest: The Formula, the Intuition and the Traps
Published · 3 min read · By The Samsung Calculator editorial team
Simple versus compound, precisely
Simple interest is paid only on the original principal. £1,000 at 5% simple interest earns £50 every year, for ever: after 30 years you have £2,500.
Compound interest is paid on principal plus all previously earned interest. The same £1,000 at 5% compounded annually reaches £4,322 after 30 years — not £2,500. The extra £1,822 is interest earning interest, and it is more than the original deposit.
The formula, term by term
A = P(1 + r/n)^(nt). P is the principal, r the annual rate as a decimal, n the number of compounding periods per year, t the number of years.
The r/n term divides the annual rate across the periods, and the nt exponent counts how many periods happen in total. Everything interesting is in that exponent: change t and the result changes geometrically, change P and it changes only in proportion. This is why starting early beats saving more, and by a wide margin.
Three numbers worth knowing
The rule of 72. Divide 72 by the annual rate to get the doubling time in years. At 6%, money doubles in about 12 years. The approximation is good between roughly 4% and 15% and is accurate enough for mental arithmetic.
Frequency matters less than people expect. £10,000 at 5% for a year yields £500.00 compounded annually, £511.62 monthly and £512.67 daily. The gap between monthly and daily is about a pound. The rate matters roughly a hundred times more than the schedule, so compare APY figures and stop worrying about the mechanism.
Time is the dominant variable. Investing £200 a month from age 25 to 35 and then stopping beats investing £200 a month from 35 to 65 at the same 7% return. Ten years of contributions beats thirty, because the first ten have thirty years to compound.
The direction people forget
Compounding runs both ways. A credit card at 22% APR compounded daily has an effective rate near 24.6%, applied to a balance that grows every day it goes unpaid. Inflation compounds too: at 3% a year, prices double in 24 years, which is why a pension projection in nominal pounds flatters the outcome badly over long horizons.
Fees compound in the same way. A 1% annual fund fee does not cost you 1% — over 30 years it removes roughly a quarter of the final balance, because every pound taken in fees is a pound that stops compounding.
See it on your own numbers
The compound interest calculator shows the split between what you contributed and what the compounding added, which is where the intuition finally lands.
Run your own numbers
Watch compounding work: the balance, the interest earned, and how much difference the compounding frequency actually makes.
About this article
Written and reviewed by The Samsung Calculator editorial team. Every calculator is written against a published formula, reviewed against at least one independent reference implementation, and dated when it changes. Last updated July 25, 2026. Spotted an error? Tell us.