I'm not sure how to do it, because normally the question provide the equation of V(t).  Am i correct if i js use d normal equation of present value?   P_t = P₀ e^rt   and  change it to   P₀ = P_t e^-rt  and assume V(t)= P_t e^-100rt         Then, differential the V(t) equation and assume dV(t)/dt = 0 to have maximum..  My working :  

ln V(t) = ln P_t + ln e^-100rt

            = ln P_t + (-100rt) ln e    Then,    

1/ V(t)  dV(t)/dt = 0 - 100r

      dV(t)/dt = V(t) [ -100r]

let dV(t)/dt = 0,

V(t) [-100r] = 0  ,   V(t) not equal to 0

-100r = 0

       r = 0   (I'm stuck here, i couldn't do the second order condition. )

I think i do somethings wrong, pls tell me where goes wrong.

Thank you very much..