Analysis - Computing Compound Return

To calculate the compounded return on an investment, just figure out the factor by which the original investment multiplied. For example, if $1000 became $3200 in 10 years, then the multiplying factor is 3200/1000 or 3.2. Now take the 10th root of 3.2 (the multiplying factor) and you get a compounded return of 1.1233498 (12.3% per year). To see that this works, note that 1.1233498 ** 10 = 3.2 (i.e., 1.233498 raised to the 10th power equals 3.2).

Here is another way of saying the same thing. This calculation assumes that all gains are reinvested, so the following formula applies:
TR = (1 + AR) ** YR
where TR is total return (present value/initial value), AR is the compound annualized return, and YR is years. The symbol '**' is used to denote exponentiation (2 ** 3 = 8).

To calculate annualized return, the following formula applies:
AR = (TR ** (1/YR)) - 1
Thus a total return of 950% in 20 years would be equivalent to an annualized return of 11.914454%. Note that the 950% includes your initial investment of 100% (by definition) plus a gain of 850%.

For those of you using spreadsheets such as Excel, you would use the following formula to compute AR for the example discussed above (the common computer symbol used to denote exponentiation is the caret or hat on top of the 6). 
= TR ^ (1 / YR) - 1 
where TR = 9.5 and YR = 20. If you want to be creative and have AR recalculated every time you open your file, you can substitute something like the following for YR: 
( (*cell* - TODAY() ) / 365) 
Of course you will have to replace '*cell*' by the appropriate address of the cell that contains the date on which you bought the security.