I have been trying to rework a common CAGR formula to be able to calculate the initial investment value if all I have if the annualized rate and the average value over the term.
So I know the standard formula is:
The formula is: R = (F/I)^(1/Y)-1
R = annualized rate
I = initial investment value
F = final investment value
Y = no of years
Avg = The average value of income over Y years
But what I have is the average value instead of the initial investment value or the final investment value.
For example, if I know the average over 5 years is $1000, and the annualized rate of return is 4%, what is the formula to compute the initial investment value?
I know by trial and error the 5 values should be:
$923.14
$960.06
$998.46
$1038.40
$1.079.94
The best formula I have found so far to create the initial value is: Avg/(1+I)^(((Y+1)/2)+LN(1+I)). From this initial value, I can multiple it and the amount each year by (1+I) and get the a close approximation to the values. But it is not exact. As the Avg value gets higher or the interest rate gets higher, the income stream deviates from the Avg I am trying to attain.
Does anyone have a better formula?
Thank you,
dmzeigler
So I know the standard formula is:
The formula is: R = (F/I)^(1/Y)-1
R = annualized rate
I = initial investment value
F = final investment value
Y = no of years
Avg = The average value of income over Y years
But what I have is the average value instead of the initial investment value or the final investment value.
For example, if I know the average over 5 years is $1000, and the annualized rate of return is 4%, what is the formula to compute the initial investment value?
I know by trial and error the 5 values should be:
$923.14
$960.06
$998.46
$1038.40
$1.079.94
The best formula I have found so far to create the initial value is: Avg/(1+I)^(((Y+1)/2)+LN(1+I)). From this initial value, I can multiple it and the amount each year by (1+I) and get the a close approximation to the values. But it is not exact. As the Avg value gets higher or the interest rate gets higher, the income stream deviates from the Avg I am trying to attain.
Does anyone have a better formula?
Thank you,
dmzeigler