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@CMCDragonkai
Created February 10, 2022 00:45
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Compound Growth (Interest) Rate

Compound Growth (Interest) Rate

Suppose something grew 300% over 20 years, and you want to know what was the annual growth rate.

Use the compound interest rate formula:

A = P(1 + r/n)^(n*t)

Where A is final amount, P is initial amount, r is the interest rate, the n is the number of times applied and t is the time periods.

You can make n = 20 and t = 1, or t = 20 and n = 1. Either way:

A/P = (1 + r/n)^(n*t)
# assume A/P is 3 due to 300% increase
# assume n is 1, and t is 20
# substitute r for g as we want the growth rate
3 = (1 + g/1)^(20)
3^(1/20) = 1 + g
3^(1/20) - 1 = g
g = 0.056
g = 5.6%
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Now calculate what the RoI each year would be, if you borrowed a proportion of the initial amount, and subtract the interest rate for the debt.

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