Exponential growth calculator
Anything that grows by a constant percentage grows exponentially, and doubles in a fixed time however large it gets.
%
Final value
2653.297 705 14
- Increase
- 1653.297 705 14
- Multiple of the start
- 2.653 297 705
- Doubling time in periods
- 14.2067
- Equivalent continuous rate
- 4.879 02 %
Show the working
- Starting value = 1000
- Growth rate per period = 5
- Periods = 20
- factor = 1 + 5/100 = 1.05
- Final value = 1000 * 1.05^20 = 2653.3
- Increase = 2653.3 - 1000 = 1653.3
- Doubling time in periods = 5 > 0 ? log(2, 1.05) : 0 = 14.2067
- Equivalent continuous rate = 1.05 > 0 ? ln(1.05) * 100 : 0 = 4.879 02
- Multiple of the start = 1000 != 0 ? 2653.3/1000 : 0 = 2.6533
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- N = N0 (1 + r)^t
- doubling time = ln 2 / ln(1 + r)