How do I calculate APR over a multi-year period?
More specifically, Annual Rate of Return.
Lets say there is a 50% increase in value of stock over a 5 year period. How do I calculate the average annual return rate?
It wouldn't be 10%, because we are assuming the return is compounded.
Lets say there is a 50% increase in value of stock over a 5 year period. How do I calculate the average annual return rate?
It wouldn't be 10%, because we are assuming the return is compounded.
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Use the future value formula in Excel! 0 -
In the formulae below, i or r are the interest rate, expressed as a true percentage (i.e. 10% = 10/100 = 0.10). FV and PV represent the future and present value of a sum. n represents the number of periods.
These are the most basic formulae:
FV = PV ( 1+i )^n\,
The above calculates the future value of FV of an investment's present value of PV accruing at a fixed interest rate of i for n periods.
PV = \frac {FV} {\left( 1+i \right)^n}\,
The above calculates what present value of PV would be needed to produce a certain future value of FV if interest of i accrues for n periods.
i = \sqrt[n]{\left( \frac {FV} {PV} \right)} -1 \,
or
i = \left( \frac {FV} {PV} \right)^\left(\frac {1} {n} \right)- 1
The above two formulae are the same and calculate the compound interest rate achieved if an initial investment of PV returns a value of FV after n accrual periods.
n = \frac {log(FV) - log(PV)} {log(1 + i)}
The above formula calculates the number of periods required to get FV given the PV and the interest rate i. The log function can be in any base, for e.g. natural log (ln)
Hope this helps.0 -
sav beat me to it.
http://en.wikipedia.org/wiki/Annual_percentage_yield0 -
I find it easier to get my head around this:
Let your buying price = B, your holding time = T, your current value = V (all of which you know) and the annual rate of return (unknown) be r
Then
V = B*r^T
V/B =r^T
Log(V/B)= T*Log(r)
(Log(V/B))/T = Log(r)
10^((Log(V/B))/T) = r
And r will be something like 1.05, meaning that you got a 5% return rate per year, on average.0 -
1-Divide the final value by the initial value.
2-Take the logarithm of the result of step 1.
3- Divide the result of step 2 by the number of years compounded. Use fractions for any months, i.e. use 7.33 for 7 years 4 months.
4- Take the anti log of the result of step 3. Example, if Ln was used in step 2 use exp.
5- subtract one. The result is the average annual compounded gain for the time period.
Multiply by 100 to have it in %.0
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