If, the next year, the return is 73%,
you multiply your starting portfolio by 1.73
Your $1.22 portfolio grows to $2.11
since $1.22(1.73) = $2.11
In general, you write the annual percentage return as a decimal
(example: 22% becomes 0.22)
then "add 1"
(example: 1.22)
then you multiply your initial portfolio by (1+return)
(example: multiply by 1.22)
For negative returns ... same thing:
Write -10% as a decimal
(so -10% becomes -0.10)
then "add 1"
(so it's now 0.90)
then you multiply your initial portfolio by 0.90
Hence, for annual returns of 22%, 73%, 21%, 45% and -10%
a $15.00 initial portfolio would grow to
$15.00*(1.22)(1.73)(1.21)(1.45)(0.90) = $49.99
That's a gain of $34.99 Since you started with $15.00, that's a total gain of $34.99/$15.00 = 2.33 or 233%
That's equivalent to what "fixed" annual return, over five years?
Suppose this "fixed" return is r (so, if r turns out to be 0123, that means 12.3%)
Then your $1.00, over these five years, would grow to
$1.00*(1+r)(1+r)(1+r)(1+r)(1+r) =
$1.00(1+r)5 which is supposed to be $3.33
Hence