Compounded Continuously Help!!! Applied Calculus

Suppose you own a parcel of land whose market price t years from now will be V(t)=20,000*e^sqrt(t) dollars. If the prevailing interest rate remains constant at 7% compounded continuously, when will the present value of the market price of the land be greatest?

A=Pe^(rt)

It's for a study guide for my last test. My professor always throws in a problem we didn't go over and I don't know where to start. Could anyone help walk me through this problem or at least let me know how to solve it?

multiply the market price times the present value equation to get a present value of the market price, so you end up with

20,000*e^(sqrt(t)) * e^(-rt) ... we can get rid of the 20,000 because that has no impact in what we are looking for

e^(sqrt(t)) * e^(-rt)
e^(sqrt(t)) * e^(-0.07t)
e^(sqrt(t) - 0.07t)

take the derivative and set equal to zero
(0.5t^(-0.5)-0.07) * e^(sqrt(t) - 0.07t) = 0

0.5t^(-0.5)-0.07 = 0
0.5t^(-0.5) = 0.07
0.5 = 0.07t^(0.5)
t = 51.02

plugging that in, the PV shows
20,000*e^(sqrt(51.02)) * e^((-.07)(51.02)) = 711368

trying 50, 52 to check it's a local maximum
20,000*e^(sqrt(50)) * e^((-.07)(50)) = 711091
20,000*e^(sqrt(52)) * e^((-.07)(52)) = 711115

No, we do not want to just differentiate the market price V(t) = 20,000*e^sqrt(t), because we need to maximize the present value, not the market price.

The present value is P(t) = V(t)e^(-0.07t) = 20,000*e^[sqrt(t) - 0.07t]. This is the function we need to differentiate.

Then set P ' (t) equal to 0 and solve for t.

you can start by finding the derivative of V(t)=20,000*e^sqrt(t)