The questions in this section contribute to your assignment grade. Stars indicate the difficulty of the questions, as described on Canvas. 2. Mark and Elyse buy a lottery ticket together. They win a promotion that guarantees them free apples for life. The apples can only be delivered to one recipient. Mark decides to buy Elyse out of her share of the win. That is: Mark will receive all the apples (for life) and Elyse will receive cash (once). The deliveries of apples are valued at $1000 per year. The friends consult an actuarial table, and decide that they both can reasonably be expected to live another 50 years. So, Elyse proposes that Mark pays her $25,000 for her half of the windfall. Mark, sensing an opportunity for calculus and for profit, declines her offer. He explains his objection: "If I pay you a dollar now, and get a dollar back 50 years later, that's not a good deal for me." Mark and Elyse agree on a future discounting rate of 10% per year. They calculate it as follows:¹ D dollars in our possession today has the same value to us as 1.1D dollars promised to us in one year, 1.12D dollars promised to us in two years, etc. We write: PV (D, t) = D 1.1t This discussion is taken from Optimal, Integral, Likely p. 317. The example in the textbook is different from the questions here, but the formula for calculating present-day value of future income is the same. 1 where PV (D, t) the the value in present-day dollars of the promise of D dollars to be paid in t years, where t and D are any non-negative real numbers. (a) Recall the model is only used with positive values of D. i. ✰✰✰✰ Interpret[PV] < 0 in terms of the model. a² PV ii. ★★☆☆ Now, interpret Ət² do not need to justify your answer. > 0. Select the best interpretation below. For this part, you A. The rate at which future income loses value over time decreases. For example: the difference between a dollar today and a dollar next year is greater than the difference between a dollar in two years and a dollar in three years. B. The rate at which future income loses value over time increases. For example: the difference between a dollar today and a dollar next year is less than the difference between a dollar in two years and a dollar in three years. C. The rate at which future income loses value over time is constant. For example: the difference between a dollar today and a dollar next year is the same as than the difference between a dollar in two years and a dollar in three years.