How compound interest works, with a worked example

Compound interest is interest that earns interest. Money set aside today earns a little, that little is added to the balance, and from then on it earns too. Over a few months the difference is hard to see. Over ten years it is most of the growth. This guide explains how it works in plain words, walks through one example with the numbers in view, and shows what it means for money a business sets aside, whether for equipment, a slow season, or next year's tax bill.

Simple interest and compound interest

With simple interest, you earn on the original amount only. $10,000 at 4% a year earns $400 every year, so after ten years you have $14,000.

With compound interest, each year's interest joins the balance. The first year still earns $400. The second year earns 4% of $10,400, which is $416. The tenth year earns $548. After ten years the balance is $14,802, and the extra $802 is interest earned by interest.

Stretch it to twenty years and the gap widens: $18,000 with simple interest, $21,911 with compound interest. The longer the money stays, the more the compounding matters, because the balance it works on keeps getting bigger.

How often the interest is added

Accounts add interest on a schedule: once a year, every quarter, every month, or every day. This is called compounding, and the more often it happens, the sooner each bit of interest starts earning.

The effect is real but smaller than people expect. At 4% a year:

• Added once a year, you earn 4.00%.
• Added every month, you earn 4.07%.
• Added every day, you earn 4.08%.

That second figure is the effective yearly rate: what you actually earn in a year once the compounding is counted. The jump from yearly to monthly is worth noticing; the jump from monthly to daily is pennies. If your bank quotes an APY, that number already includes the compounding, so it is the effective rate.

The formula

For a single amount, the future value is the amount times (1 + i) raised to the power of N, where i is the rate per period and N is the number of periods. At 4% a year added monthly, i is 0.04 divided by 12, which is 0.003333, and ten years is 120 periods.

$5,000 × (1.003333)^120 = $5,000 × 1.4908 = $7,454.

For money added at the end of every period, the future value is the amount times ((1 + i)^N − 1) divided by i. Adding $300 a month for the same ten years:

$300 × (1.4908 − 1) ÷ 0.003333 = $300 × 147.25 = $44,175.

Together: $7,454 + $44,175 = $51,629. You put in $41,000 over the ten years; the other $10,629 is growth.

You do not have to do this by hand. The compound interest calculator takes the same inputs, shows the result, and lists every month or year in a table you can download.

The same example, year by year

Seeing the growth line change is what makes compound interest click:

• Year 1: you add $3,600, the balance earns $270, and ends at $8,870.
• Year 5: you still add $3,600, but the balance earns $941.
• Year 10: the same $3,600 in, and the balance earns $1,944, seven times the first year.

Nothing about the deposits changed. What changed is the balance doing the earning. Keep going five more years and the total reaches $82,929, with $23,929 of growth. Those last five years earned $13,300, more than the first ten years combined.

Those last five years earned $13,300, more than the first ten years combined.

The rule of 72

A quick check you can do in your head: divide 72 by the yearly rate, and you get roughly the number of years it takes money to double. At 4%, about 18 years. At 6%, about 12. At 3%, about 24.

It is a rule of thumb, not a formula, and it works best for rates in the single digits. It also runs backwards: to double in ten years, you would need about 7.2% a year.

What it means for money a business sets aside

• Start the habit before the amount is impressive. In the example, the monthly $300 did more than the rate did. Time and regular additions are the two things you control.
• Keep it separate. A reserve in its own account, named for its purpose, earns its interest in plain sight and is harder to spend by accident.
• Interest is usually taxable. The calculator leaves taxes out. Your monthly books record the interest the account pays, so it is ready at tax time rather than a surprise.
• Inflation works the other way. A dollar in ten years buys less than a dollar today. If you type an inflation rate into the calculator, it also shows the result in today's dollars.
• It cuts both ways. A credit card or a loan that compounds grows the same way against you, which is why paying a balance down early saves more than the rate alone suggests.

Want a second pair of eyes on the numbers?

If you would like to talk through what your business could set aside each month, and how to keep the books simple while it grows, start a conversation. We work in English and Spanish.

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Written by the team at Choice Business Advisors, a bookkeeping, tax, and advisory firm based in Utah serving small businesses across the United States in English and Spanish.