Compounding
1,000 invested at 7 percent a year, compounded once a year. The rate is an assumption for the arithmetic, not a forecast.
Year 0 of 40

0

after 0 years at 7 percent a year, compounded annually

72The rule of 72, checked against the exact doubling time

Divide 72 by the rate and the answer is, roughly, the years it takes money to double. The rungs of the ladder are drawn at the exact doubling time, ln 2 divided by ln(1 + r); the dashed tick beside each rung is 72 divided by the rate, so the error of the shortcut is visible on the rail.

Compounding

Back to year 0

Assumption

1,000 at 7 percent a year, compounded once a year, with no contributions, withdrawals, taxes or fees. The 7 percent is an input chosen for the arithmetic; it is not a forecast of any market or asset.

Formulas

Compound balance after n years: 1,000 × (1 + 0.07)n. Simple interest: 1,000 × (1 + 0.07 × n). Exact doubling time at rate r: ln 2 ÷ ln(1 + r). Rule of 72: 72 ÷ (100 r).

Source

Every figure on this page is computed by the page's own script from the formulas above and rounded to the nearest whole unit for display; no market data is used. The curves are drawn continuously; with annual compounding the balance actually moves in yearly steps.