Guide · Use with the APR / APY Interest Converter and the Retirement Runway Calculator

Compound Interest Explained, With Worked Examples

Last reviewed: 31 October 2026 · How we check our calculations
Every figure on this page is arithmetic you can check; no official rates are quoted.

Compound interest means you earn interest on your interest. Over a year the effect is small. Over twenty or thirty years it decides most of the final balance. This guide shows the formula in plain English, works through examples you can check yourself, and explains how the CashOutline tools use the same maths.

Simple interest and compound interest

With simple interest, you earn interest only on the money you put in. ฿100,000 at 2.4% a year earns ฿2,400 every year, so after ten years you have ฿124,000.

With compound interest, each interest payment is added to the balance and earns interest itself from then on. The same ฿100,000 at 2.4% a year, compounded monthly, grows to ฿127,094 after ten years. The extra ฿3,094 is interest earned on earlier interest.

The formula in plain English

• Annual rate is the nominal rate (the APR) as a decimal, so 2.4% is 0.024.
• Periods per year is how often interest is added: 1 for yearly, 4 for quarterly, 12 for monthly, 365 for daily.
• The ^ means "to the power of": multiply the bracket by itself that many times. A spreadsheet or phone calculator does this for you.

For one year, the formula gives the APY, the effective annual rate. That is exactly what the APR / APY converter calculates: APY = (1 + APR ÷ n)ⁿ − 1.

Worked example: a Thai savings deposit

฿100,000 at 2.40% a year, compounded monthly.

The one-year figure matches the converter: enter 2.40, APR, Monthly, and it shows an APY of 2.427%.

Time does most of the work

At low rates and over short periods, compounding hardly matters. Over long periods it dominates. Here is $10,000 left to grow at 5% a year, compounded yearly, for 30 years:

Two points stand out. Compounding adds $18,219 over simple interest at the same 5%. And two extra percentage points of return add another $32,903, because the higher rate compounds for the whole 30 years. Small differences in rates or fees matter most over long periods.

Compounding frequency matters less than you might think

Banks sometimes advertise daily compounding as a selling point. Here is $10,000 at 5% a year for 10 years:

Moving from yearly to monthly is worth $181 here. Moving from monthly to daily is worth $17. Compare savings accounts on APY, which already includes the compounding, and don't let the compounding frequency decide on its own.

Adding regular savings

Most people don't invest a lump sum and walk away; they add money every month. The Retirement Runway Calculator handles this with the standard future-value formula, compounding once a year and adding each year's contributions at the end of the year:

Here r is the yearly return and n is the number of years. Using the calculator's own worked example: $100,000 already saved, plus $600 a month ($7,200 a year), at 5% for 22 years.

You would have paid in $158,400 of new money. Compounding turns it into $277,238. Because the calculator adds contributions at the end of each year, it is slightly cautious: money added monthly and compounded monthly would grow to about $287,600.

Two shortcuts worth knowing

The rule of 72

Divide 72 by the yearly rate to estimate how many years it takes money to double. At 6%, 72 ÷ 6 = 12 years; the exact answer is 11.9. At 2.4%, the rule gives 30 years; monthly compounding makes it 28.9. It is an estimate, best between about 2% and 10%.

Real returns after inflation

A balance that doubles while prices also double has bought you nothing. To see growth in today's money, use the real return:

A 7% return with 3% inflation is a real return of 1.07 ÷ 1.03 − 1 = 3.88%, slightly less than the 4% you get by subtracting. The retirement calculator asks for a return after inflation because it keeps your spending target in today's dollars.

Common mistakes

• Mixing up APR and APY. The formula needs the nominal rate (APR) and the compounding frequency. If you start from an APY, convert it first.
• Projecting with a nominal return and comparing with today's prices. Either use a real return, or remember to shrink the result for inflation.
• Treating the projected balance as certain. Investment returns vary from year to year. A fixed rate is a planning assumption, not a promise.
• Forgetting fees and tax. A 1% yearly fee takes roughly one percentage point off the rate in the formula, and its cost compounds too.
• Using the formula for loans you repay in instalments. Your balance falls as you repay, so the simple growth formula overstates the interest. For flat-rate loans, see the flat-rate loans guide.

Questions people ask

Does compound interest work against me on debt?

Yes. On a credit card, unpaid interest is added to the balance and then charged interest itself. A card charging 2% a month costs 26.82% a year once that compounding is counted.

How often does my bank compound?

It varies by bank and product, so check the terms. Comparing on APY makes the question mostly irrelevant, because APY already includes the compounding.

Is a higher compounding frequency worth switching banks for?

Rarely. As the table above shows, the gap between monthly and daily is tiny. A higher APY, lower fees or better access to your money usually matter more.

Related tools and guides

• APR / APY Interest Converter: turn any quoted rate into an APY and compare two offers.
• Retirement Runway Calculator: project savings with regular contributions to your retirement age.
• The 4% rule: what happens when you start drawing the money down.

The rates in this guide are examples chosen to show the arithmetic, not forecasts or offers. This guide explains how interest works. It is not financial advice. How we check our calculations.