Useful Utilities

Interest Rate Calculator

Annual effective rate from observed growth, the Rule of 72 checked against exact doubling rates, and the rate needed to reach a goal over a horizon.

Fill in the values and calculate

ModeDefault Annual rate from observed growth
Start valueAny unit; only the ratio to the end value mattersDefault 1000
End value or goalValue reached (goal mode: value to be reached)Default 2000
Years (elapsed / doubling time / horizon)How long it took, or how long you haveDefault 10

The form sends itself back to this page — results print below, computed on the server.

No results yet: fill the form above and press Calculate.

About Interest Rate Calculator

Three ways to get the annual compounding rate from numbers you have: the rate an investment actually grew at over a period, the rate implied by the time it took to double, and the rate you must beat to reach a goal. All three use the same exact math: rate = (end / start)^(1 / years) - 1.

The doubling pages put the Rule of 72 side by side with the exact rate: a chart over one to twelve years, a table of the rate and the shortcut, and the gap in percentage points.

Questions about Interest Rate Calculator

Why does it show two rates a year?

The effective annual rate is the growth you actually get; the nominal APR is the number banks print when that growth is delivered by monthly compounding. Same growth, different quoting convention.

Is the Rule of 72 ever exact?

It is closest for rates around six to ten percent a year — its error is largest at the extremes. The table shows the exact figure and the shortcut side by side, and the generalized rule 72 x log2(multiple) / time works for any multiple.

What is a doubling time?

How long a value takes to double at a rate: ln 2 / ln (1 + rate). A negative figure is a halving time instead, which is why decay rates read out that way.

Does the currency unit matter?

No. The math only ever looks at the ratio between the start and end values, so any consistent unit works.

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