Question

consider how to solve for the return on investment for an asset that was invested for only a fraction of a year - e.g., for only 50% of a year.. We can do the same for multi-year investments for which we are interested in obtaining a return measure that considers the time value of money. what do you think...?  

Answer 1

Ending value of investment = beginning value * (1 + r)n

where r = annual rate of return

r = number of years.

In this equation, "r" could be less than 1 year, or it could be multiple years.

For example, let us take the following example :

Ending value of investment = $102.25

Beginning value = $100.00

n = 50% of year, or 0.50.

Ending value of investment = beginning value * (1 + r)n

$102.25 = $100.00 * (1 + r)0.50

r = (102.25 / 100.00)1/0.50 - 1

r = 0.0455, or 4.55%

In this way, we can  solve for the return on investment for an asset that was invested for only a fraction of a year