Maps for Math

Why do I need exponents to understand compound interest?

Compound interest pays interest on your interest, so money grows by a factor each period instead of a fixed amount. Repeated multiplication is an exponent. That's why the balance curves upward, and why starting ten years earlier can matter more than saving twice as much. The same exponent makes debt grow just as fast.

simple interest $8,000.00$9,103.77
You’ll have
$9,103.77
Interest earned
$4,103.77
Doubles every (years)
23.1

Challenge: Double your money.

$
%
More settings

Play

Stretch the years out. Watch the curve bend upward away from the straight line.

Challenge: Double your money. The box under the picture turns green when you get it.

Stuck? Pick one of the examples from the “Try an example” menu, or press “New example.”

Understand

A=P(1+rn)ntA = P\left(1 + \frac{r}{n}\right)^{nt}

Each period the balance is multiplied by 1+r/n1 + r/n. Do that ntnt times and you get an exponent:

A=P(1+rn)ntA = P\left(1 + \frac{r}{n}\right)^{nt}

The dashed straight line is simple interest, which adds the same dollars every year. The curve is compound interest, which adds the same percent. Early on they look alike. Over decades the curve pulls far ahead, because each year's interest is bigger than the last.

Use

Every input has a unit menu, so you can type values in the units you already have. Results follow your units.

Show the work

  1. Compound interestA = P\left(1 + \frac{r}{n}\right)^{nt}
  2. With your numbersA = 5000\left(1 + \frac{0.03}{12}\right)^{12 \cdot 20}
  3. ResultA = \$9103.77,\quad \text{interest} = \$4103.77
  4. Doubling timet_2 = \frac{\ln 2}{n \ln(1 + r/n)} \approx 23.13\ \text{years} \quad (\text{rule of 72: } 24)

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Enter a starting amount, rate, and number of years. Choose how often interest is added in "More settings." The doubling time uses logarithms: t=ln⁡2/(nln⁡(1+r/n))t = \ln 2 / (n\ln(1 + r/n)).

  • Real returns vary year to year. Treat long-run rates as averages, not promises.
  • Inflation shrinks what the final amount can buy. Subtract it from the rate for a rough "real" answer.

For learning and estimation. Verify with applicable codes, standards, and a qualified professional before using in design, construction, or safety-critical work.

Cheat card

A=P(1+rn)ntA = P\left(1 + \frac{r}{n}\right)^{nt}
tdouble≈72r (%)t_{\text{double}} \approx \frac{72}{r\,(\%)}
SymbolMeaningUnit
PPstarting amount$
rryearly rate as a decimal
nntimes interest is added per year
ttyears
  • Rule of 72: divide 72 by the rate to estimate the doubling time.
  • Time matters more than rate. Early years get the most doublings.
  • More frequent compounding helps, but only a little.

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Where it’s used

  • Finance & Business
    Banks, investors, and lenders price savings accounts, loans, and retirement plans with this formula.
  • Money & Shopping
    It shows why credit card balances snowball, and why early saving pays off.

Questions people ask

What is compound interest?

Interest that is added to your balance, so the next round of interest is calculated on a bigger amount. It grows by multiplying, not adding.

What is the rule of 72?

A shortcut for doubling time. Divide 72 by the interest rate in percent. At 8%, money doubles in about 9 years.

Does compounding monthly instead of yearly make a big difference?

A small one. At 7% for 30 years, monthly compounding gives about 8% more than yearly. The rate and the number of years matter much more.

Sample EXP-0001 · rev 1 · model EXP-M01 · Level 3 · algebra · updated 2026-09-24