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%
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.