Find & interpret an expression for the point in time at which the present value of the portfolio is at maximum

Question

The market value (V) of a portfolio grows over time according to the function §(t) where d§(t)/dt > 0. The present value of the portfolio is given by V=§(t) e^-rt. Find and interpret an expression for the point in time at which the present value of the portfolio is at it's maximum...

Answer 1

Looking at the equation for V, the 'power' is shown as a negative.

Thus V = 1 divided by (e to the power of r t )

This means the Value will reduce as time ( t ) increases.

So, by inspection, the maximum is when t=0.

At this time, V = 1.

Answer 2

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