Since ROI (simple interest) is return with no reinvestment and CAGR with re-investment and g (<1) being the rate at which more vehicles are added,
CAGR = ROI + ROI*g + ROI*g^2 + ROI*g^3 + .......to infinity
CAGR = ROI (1+g + g^2 + g^3 +.....)
The sum in the bracket is sum of infinite geometric series = 1 / (1-g)
CAGR = ROI / (1-g)
So, CAGR with complete reinvestment corresponding to 50% growth in vehicles is
15 / (1-0.5) = 30
For 30% growth in vehicles,
15 / (1-0.3) = 21.5%
And so on...
CAGR = ROI + ROI*g + ROI*g^2 + ROI*g^3 + .......to infinity
CAGR = ROI (1+g + g^2 + g^3 +.....)
The sum in the bracket is sum of infinite geometric series = 1 / (1-g)
CAGR = ROI / (1-g)
So, CAGR with complete reinvestment corresponding to 50% growth in vehicles is
15 / (1-0.5) = 30
For 30% growth in vehicles,
15 / (1-0.3) = 21.5%
And so on...
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