posted by illy on .
Suppose that the dealer, who is 25 years old, decides to sell the card at time , sometime in the next 40 years: 0< or equal to t < or equal to 40. At that time , he’ll invest the money he gets for the sale of the card in a bank account that earns an interest rate of r , compounded continuously. (This means that after years, an initial investment of will be worth Ie^(rt).) When he turns 65, he’ll take the money that’s in his bank account and begin to draw on it for his retirement. Let A be the amount of money in his account when he turns 65.
Plot the function A(t) for several different values of k, while holding r constant. What does a larger value of k imply about the value of the card over time?. And now, what does a larger value of k imply about the best time to sell the card? Do these two facts seem consistent with one another?