Chapter 5.4, Problem 77E

Optimal Selling Time Refer to Exercise 49, page 367. The present value of a piece of waterfront property purchased by an investor is given by the function

$P(t)=80,000e^{\sqrt{t}/2-0.09t}(0\le t\le 8)$

Determine the optimal time (based on present value) for the investor to sell the property. What is the property’s optimal present value?

49. Real Estate Investments An investor purchased a piece of waterfront property. Because of the development of a marina in the vicinity, the market value of the property is expected to increase according to the rule

$V(t)=80,000e^{\sqrt{t}/2}$

where V(t) is measured in dollars and t is the time in years from the present. If the rate of appreciation is expected to be 9% compounded continuously for the next 8 years, find an expression for the present value P(t) of the property’s market price valid for the next 8 years. What is P(t) expected to be in 4 years?