Example
If an investment increases in valve in 2 years from $100 to $125, the increase of $25 in the 2 years period would represent a cumulative return of 25%. But how would you calculate the annualised rate of return ? What is the formula ?
stock analyst
Comments
Was the rate of return consistent throughout the 24-month period? Monthly compounding formula for 24-month period is (1+rate/12)^24.
I think you want the inverse of this to the 12th power:
12 * ( e^ ( ln(1.25) / 24 ) -1 )
Correct me if this is wrong…
The formula is P*(1+i)^n= A
n= number of years, i= interest rate, P= principal amount and A=ending amount
You know A, n, and P. What you do not know is i. So solve for i.
(1+i) ^n = A/P
n*log(1+i) = log A/P
log(1+i)= (log A/P)/n
then take the anti log of the result and you get i= 11.8%
It helps to have a calculator that can pefor log functions. Or you can use a spread sheet.
Muncie birder’s answer is correct, but there’s a quicker way to calculate it: (Final value/initial value) ^ (1/# of years)
In this case:
(125/100) ^ (1/2) = 1.25 ^ 0.5 (i.e. 1.25 to the 0.5 power) = 1.118.
Subtract 1 from that and multiply by 100 to get it in percent (11.8%).
It’s really quite simple. As you noted, you had a25% return over a 2 year period. The annualized is $25%/2 or 12.5%. For my personal knowledge, that’s close enough for me.
///
Calculation.
Average annual rate = sq. rt 1.25 - 1 = 11.8 %
((TotalReturn + 1 ) ^ (252 / (MarketDays)) - 1
Here is the site that fully defines the terms. the ^ means raise to the power (exponentiation)
If you want to use calendar days instead of market days change 252 constant to 365
