Compound Interest Calculator

How compounding works

Compound interest is interest earned on interest. Each period, the interest calculated is added to the balance, and the next period's interest is calculated on that larger balance. Over a long enough horizon this dominates everything else about an investment, including the rate itself.

The exponent is what does the work. Because the rate sits inside a power rather than a product, small changes in r or t produce disproportionate changes in the outcome.

A worked example

You invest 200,000 at 9% per annum, compounded quarterly, for 10 years.

• Rate per period: 0.09 / 4 = 0.0225
• Number of periods: 4 x 10 = 40
• A = 200,000 x 1.0225^40 = 200,000 x 2.4352 = 487,040
• Interest earned: 287,040 — more than the original investment

The same money at simple interest would have earned 180,000. The extra 107,040 is entirely the effect of interest earning interest.

Compounding frequency

More frequent compounding produces a higher return, but the effect saturates quickly. Here is 100,000 at 10% for one year at different frequencies:

The jump from annual to monthly is worth about half a percent; the jump from monthly to daily is worth four hundredths. Anyone advertising daily compounding as a headline feature is selling you a rounding error. The number that lets you compare products honestly is the effective annual rate, which folds the frequency into a single figure:

The rule of 72

To estimate how long money takes to double, divide 72 by the annual percentage rate. At 8% that is 9 years; at 12%, 6 years; at 6%, 12 years. The approximation is good between roughly 5% and 15% and drifts at the extremes, but it is accurate enough to do in your head and it makes the cost of a lower rate immediately obvious. An investment at 6% doubles twice in 24 years; at 12% it doubles four times, ending up four times larger from the same starting point.

Time matters more than rate

Because t sits in the exponent, starting earlier beats earning more. Two people each invest 100,000 once and leave it at 10%:

• One invests at age 25 and stops. By 65, 40 years later, it is worth 4,525,926.
• The other invests at age 35. By 65, 30 years later, it is worth 1,744,940.

A ten-year delay costs more than the entire principal several times over. This is the arithmetic behind most retirement advice, and it is also why compounding is so punishing on the other side of the ledger: credit card debt at 3% monthly compounds to an effective 42.6% a year.

What this calculation leaves out

• Inflation. The result is nominal. To get real purchasing power, subtract inflation from the rate before calculating: 9% growth with 5% inflation is closer to 3.8% real, not 4% — the correct adjustment is (1.09 / 1.05) - 1.
• Tax. Interest, dividends and capital gains are usually taxable, and tax paid each year rather than at the end removes money that would otherwise have compounded.
• Fees. An expense ratio compounds against you exactly as returns compound for you. A 1% annual fee over 30 years consumes roughly a quarter of the final balance.
• Regular contributions. This tool compounds a single lump sum. For a monthly investment plan, use our SIP calculator, which handles a stream of deposits.
• Variable returns. A fixed rate is a modelling assumption. Real market returns vary, and the sequence in which good and bad years arrive affects the outcome when you are also adding or withdrawing money.

Frequently asked questions