Problem:
Optimizing Net Present Value Using Continuous Compounding
The value of good wine increases with age. Thus if you are a wine dealer, you have the problem of deciding whether to sell you wine now, at a price of $P a bottle, or sell it later at a higher price. Suppose you know that the amount a wine-drinker is willing to pay for a bottle of wine t years from now is $P(1+20(sqr(t))). Assuming continuous compounding and a prevailing interest rate of 5% per year, when is the best time to sell your wine?