Compound Interest Calculator

A = P (1 + r/n)^(n·t)

What is compound interest?

“Compound interest is the eighth wonder of the world. He who understands it, earns it; he who doesn’t, pays it.” — Albert Einstein

Compound interest is interest that earns interest. Each period your balance grows by the interest rate, and the next period’s interest is calculated on that larger balance — not just on your original deposit. That feedback loop is why a compounding balance curves upward over time instead of rising in a straight line.

In the formula above, P is the principal (your starting amount), r is the annual interest rate as a decimal, n is how many times interest is compounded per year, and t is the number of years. Simple interest pays only on the original principal, so the gap between the two starts small and then widens dramatically.

Worked example — $10,000 at 8% a year, compounded annually: After year 1: 10,000 × 1.08 = $10,800 After year 2: 10,800 × 1.08 = $11,664 (you earn $864, not $800 — the extra $64 is interest on year one’s interest) After 20 years: 10,000 × 1.08^20 ≈ $46,610 Simple interest would have paid only 10,000 + 20 × 800 = $26,000 over the same period.

Adding regular contributions

Most people do not leave a lump sum untouched — they keep adding to it. A regular deposit, monthly or yearly, turns the calculation into an annuity: each contribution starts compounding from the moment it is paid in, so earlier deposits grow more than later ones.

With level contributions the future value adds an annuity term to the formula above: PMT × [((1 + r/n)^(n·t) − 1) ÷ (r/n)], where PMT is the amount paid each period. The longer a contribution has been invested, the more it is worth at the end — which is the real case for starting early rather than saving more later.

Worked example — $10,000 start, plus $200 a month for 20 years at 8% (monthly compounding): The lump sum alone grows to ≈ $49,270. The $200 monthly deposits ($48,000 paid in) grow to ≈ $117,800. Total ≈ $167,100 — about $109,100 of that is interest, and only $58,000 is money you actually paid in.

Inflation and tax

A big future number is not the same as a big amount of spending power. Inflation erodes what each unit of currency buys, so a balance that looks large in twenty years may buy far less than it appears. To compare fairly, discount the future value back to today’s money by dividing by (1 + inflation)^t — the calculator’s “real value” figure does exactly this.

Tax takes a second bite: in most places the interest you earn is taxable, either each year or on withdrawal, which lowers what you keep. Enter a tax rate and an inflation rate under Advanced options and the calculator shows the after-tax balance and its real, inflation-adjusted value side by side.

Worked example — a $46,610 balance after 20 years: At 3% average inflation, dividing by 1.03^20 (≈ 1.806) leaves about $25,800 in today’s purchasing power. If the $36,610 of interest is taxed at 20%, that is roughly $7,320 in tax — an after-tax balance near $39,290 before adjusting for inflation.

Frequency, time, and a rule of thumb

Compounding frequency matters, but less than people expect. The same 8% nominal rate compounded monthly rather than annually lifts the 20-year result by only a percent or two, and daily compounding adds barely anything more. The headline rate and the number of years dominate everything else.

Time is the lever that does the heavy lifting. Because early money compounds for the longest, doubling your time horizon usually beats doubling your contribution. A quick shortcut is the Rule of 72: divide 72 by the annual rate to estimate the years it takes money to double — about nine years at 8%, about twelve at 6%.

Assumptions

• Contributions are made at the end of each period.
• The rate is constant; any tax applies only to interest earned, and inflation discounts the result to today’s purchasing power without changing the nominal balance.
• Compounding frequency is applied exactly as selected.