Compound interest explained with simple examples

Compound interest is often described as interest on interest. The idea is simple, but its effect over long periods surprises most people. Understanding it helps you compare deposits and investments, see why starting early matters, and also see why expensive debt grows so fast. This guide uses hypothetical round numbers in soʻm to show how it works.

Simple interest and compound interest

With simple interest, you earn interest only on the amount you put in at the start (the principal). With compound interest, the interest you earn is added to the balance, and from then on it earns interest too.

A hypothetical example: suppose you put 1,000,000 UZS somewhere that pays 10% a year, and you leave everything untouched.

• With simple interest, you earn 100,000 UZS every year. After 10 years you have 1,000,000 + 10 × 100,000 = 2,000,000 UZS.
• With compound interest, the first year also earns 100,000 UZS, giving 1,100,000 UZS. In the second year you earn 10% of 1,100,000, which is 110,000 UZS, giving 1,210,000 UZS. The amount earned grows every year. After 10 years you have about 2,594,000 UZS.

The difference, about 594,000 UZS, is the interest earned on earlier interest. Over longer periods it grows much larger. In the same hypothetical example, after 20 years compounding gives about 6,727,000 UZS, compared with 3,000,000 UZS under simple interest. After 30 years it is about 17,449,000 UZS.

The general formula is:

• Final amount = principal × (1 + rate) ^ number of years

For 10 years at 10%, that is 1,000,000 × 1.1 ^ 10, which a phone calculator or spreadsheet can do in a second.

The rule of 72

A handy shortcut tells you roughly how long it takes for money to double at a given annual rate:

• Years to double ≈ 72 ÷ annual rate in percent

At 10% a year, money doubles in about 72 ÷ 10 = 7.2 years. At 6% it takes about 12 years; at 12%, about 6 years. The rule is an approximation, but it is close enough for quick comparisons.

It works in reverse too. If prices rise by 8% a year, the purchasing power of cash that earns nothing halves in about 72 ÷ 8 = 9 years. That is why inflation matters so much, as explained in inflation and your savings.

How often interest is added

Interest can be added (capitalised) yearly, quarterly, monthly or even daily. The more often it is added, the sooner it starts earning interest itself.

A hypothetical example: a rate of 12% a year added once a year gives exactly 12% after one year. The same 12% added monthly, 1% each month, gives about 12.68% after one year, because each month's interest earns interest in the following months.

When you compare bank deposits in Uzbekistan, read the terms carefully. Check whether the interest is capitalised (added to the deposit) or paid out to you, how often this happens, and what happens if you withdraw early. Two deposits with the same headline rate can give different results.

Regular saving and the value of time

Most people do not invest one lump sum. They add money every month. Compounding works on each of these amounts from the moment it goes in.

A hypothetical example: you save 100,000 UZS every month for 10 years, and your savings grow at 10% a year, compounded monthly. You put in 12,000,000 UZS in total, and at the end you have about 20,480,000 UZS. If you keep going for 20 years, you put in 24,000,000 UZS and end up with about 75,900,000 UZS. Doubling the time more than triples the result, because the early deposits have much longer to grow.

These examples assume a steady return every year, which is not how real investments behave. Deposits pay a known rate only for their term, and share and bond prices go up and down. The point is not the exact figure but the shape: time and regularity matter more than trying to pick the perfect moment.

Two practical lessons follow:

• Start early, even with small amounts. Waiting a few years to start with a larger sum often ends up with less than starting now with a smaller one.
• Reinvest income. If you hold shares that pay dividends or bonds that pay coupons, reinvesting that income is what turns simple returns into compound ones. Our guide to P/E, dividends and dividend yield and to bond yield, coupon and price explain where that income comes from.

What works against compounding

Compounding amplifies everything that reduces your return, not only the return itself.

• Fees. A fee of a few percent a year sounds small, but it is taken every year from a growing balance. In a hypothetical example, 1,000,000 UZS growing at 8% a year becomes about 2,159,000 UZS after 10 years, but at 6% (the same return minus 2% of fees) only about 1,791,000 UZS.
• Inflation. What matters is your real return, the growth above inflation. If your savings grow 10% a year but prices rise 8% a year, your purchasing power grows only about 2% a year.
• Taxes. Tax on interest, dividends or gains reduces what stays invested. Check current rules in the Tax Code on lex.uz.
• Losses. A fall of 50% needs a rise of 100% to get back to where you started. Avoiding large losses, for example by spreading your money across several investments, protects the compounding process. See diversification and risk.
• Debt. Compounding works against you on loans. Unpaid interest on a credit card or consumer loan can be added to what you owe, so the debt grows faster than many people expect. Paying down expensive debt is often the most reliable return available.

Trying it yourself

The best way to feel compounding is to run your own numbers. Take an amount you could realistically save each month, a return you consider cautious, and a period of 10, 20 and 30 years, and put them into a spreadsheet. Then change one input at a time: the rate, the monthly amount, the number of years.

For real-world inputs, the Central Bank of Uzbekistan (CBU) publishes its policy rate on cbu.uz, and the national statistics agency publishes inflation on stat.uz. On Finmind, you can look up any UZSE share on the public stocks pages and any listed bond on the UZSE bonds pages to see prices and, where they are published, dividends per share and coupon terms. If you create a free Finmind account, the simulator lets you practise building a portfolio with virtual money, and the free tutorials include a lesson on compounding.

This article is for education only and is not investment advice. Investing in securities involves risk, including the loss of money you invest.