Suppose you have inherited an antique whose current market value is $500. Let us assume that the market value will increase steadily at a rate of $100 per annum, and that interest on a bank deposit will be compounded continuously at the equivalent annual rate of 5%. Write down the expression for the present value of the amount realised by selling the antique after t years, and determine the optimum time to sell (assuming you can find someone to buy it then, at the market value.)