Compound interest: how it works, formula and examples

What compound interest is

Imagine you put UAH 100,000 into an account at 10% a year. In the first year the bank pays UAH 10,000. If that money stays in the account, in the second year interest is calculated on UAH 110,000, and you get UAH 11,000. In the third year, UAH 12,100. The interest starts earning interest of its own.

That is compound interest, also called capitalisation. The opposite is simple interest: income is always calculated on the original amount only and is the same every year. With simple interest the same UAH 100,000 would bring exactly UAH 10,000 a year, forever.

In the first years the difference is barely visible. But it accumulates, and over a long horizon it becomes huge.

UAH 100,000 at 10% a year: simple vs compound interest (compounded yearly)
Term	Simple interest	Compound interest	Difference
10 years	UAH 200,000	UAH 259,374	+UAH 59,374
20 years	UAH 300,000	UAH 672,750	+UAH 372,750
30 years	UAH 400,000	UAH 1,744,940	+UAH 1,344,940

Notice: in the first 10 years compound interest gave “only” 59 thousand more. Over 30 years it gave 1.3 million more. No new deposits, the same rate. The whole difference comes from time.

The formula in plain words

Banks and calculators use one formula for compound interest. It looks scarier than it is.

In words: divide the annual rate by the number of compounding periods, add one, and raise it to the power of “how many times over the whole term interest is added to the balance”. For UAH 100,000 at 10% for 10 years compounded yearly: 100,000 × 1.1¹⁰ = UAH 259,374.

How often interest compounds also matters, though it is not decisive. The same UAH 100,000 at 10% for 10 years gives UAH 259,374 compounded yearly, UAH 268,506 quarterly and UAH 270,704 monthly. So when you compare deposits with the same rate, choose the one that compounds more often.

The rule of 72: how fast your money doubles

To avoid working out powers in your head, there is a simple rule: divide 72 by the annual rate in percent and you get roughly how many years it takes for money to double.

at 6% a year: 72 / 6 = 12 years;
at 8%: 72 / 8 = 9 years;
at 10%: 72 / 10 = 7.2 years (7.27 exactly);
at 12%: 72 / 12 = 6 years.

The rule also works in reverse: with inflation at 8% a year, the purchasing power of cash kept under the mattress halves in about 9 years. Compounding works for you and against you in exactly the same way. The inflation calculator shows what this looks like for your own money.

Regular deposits: how UAH 1,000 a month turns into 759 thousand

Most people don't have a large sum upfront; they save part of their income every month. Compound interest works the same way here: every new deposit starts earning, and accrued interest is added to the balance every month.

The first years feel pointless: after five years the account holds about 77 thousand, of which only 17 is interest. But by year 8 the interest earned in a year (about UAH 13,200) is already more than you deposit yourself (UAH 12,000), and in year 20 it brings in over UAH 69,000. From then on the money mostly grows by itself.

Why time matters more than amount: starting at 25 vs 35

The power of time is easiest to see by comparing two people with the same habits who started at different ages.

Olena starts saving UAH 1,000 a month at 25 and keeps going until 60. Andrii saves the same amount but starts at 35. Both earn 8% a year, compounded monthly.

UAH 1,000 a month at 8% a year until age 60
	Olena (from 25)	Andrii (from 35)
Years of deposits	35	25
Own money deposited	UAH 420,000	UAH 300,000
Interest	UAH 1,873,882	UAH 651,026
Balance at 60	UAH 2,293,882	UAH 951,026

Olena deposited only UAH 120,000 more but ended up with 1.34 million more, 2.4 times as much. To catch up, Andrii would have to save about UAH 2,410 a month instead of 1,000, more than twice as much.

An even more telling case: if Olena saved for only 10 years, from 25 to 35, and then simply left the account alone, at 60 she would have about UAH 1,342,856. That is more than Andrii has, even though she put in UAH 120,000 against his 300,000. The first ten years keep working longer than all the years that follow.

What eats into compound interest

The formula shows an ideal picture. In practice several things reduce the result, and you should account for them.

Inflation

If a deposit pays 12% a year and prices rise by 8%, the real return is about 4%. The real return is what shows how much more you will be able to buy with your money in the future. The National Bank of Ukraine publishes current inflation data.

Taxes

In Ukraine, personal income tax and the military levy are withheld from deposit interest and other passive income. Check current rates and exemptions (for example, for government bonds) on the State Tax Service website. For a quick calculation, simply reduce the rate by the share taken by tax.

Withdrawals and breaks

Every withdrawal removes not only the amount but also all future interest on it. That is why long-term savings should be kept separate from money for current spending, with an emergency fund for the unexpected.

Fees

A difference of 1-2% a year looks minor, but over 20-30 years it takes a noticeable part of the result, through the same compounding working in reverse.

How to make compound interest work for you

Start now, even with a small amount. UAH 500 a month from age 25 often gives more than UAH 1,500 from 40.
Automate. Set up an automatic transfer to a separate account on payday, so the money is saved before you have time to spend it. How to choose the amount is covered in our article on the 50/30/20 rule.
Reinvest the income. Choose options with compounding and don't withdraw accrued interest.
Don't interrupt the process. The last years, when the balance is already large, are the most valuable. A break in the middle costs more than it seems.
Watch the real return. Compare the rate with inflation and account for taxes and fees.
Don't chase promises. A high “guaranteed” return is a reason to be cautious. Compound interest works at moderate rates over a long time.

In short

Compound interest is interest on interest; over a long term it produces most of the result.
Rule of 72: divide 72 by the rate to get roughly how many years it takes to double your money.
UAH 1,000 a month at 10% for 20 years is UAH 759,369, of which UAH 519,369 is interest.
Starting 10 years earlier matters more than contributing twice as much later.
Inflation, taxes, fees and withdrawals reduce the real result; include them in your calculations.

Sources

This article is for information only and is not financial or investment advice. Check current terms with your bank or financial institution before making decisions.