1. Maturities and Present Values. Present values capture how much a stream of payoffs is worth, taking into account how far in the future those payoffs will be received. It stands to reason that, as time goes on, the present value of an asset will change. This question asks you to think about how that can happen. (a) Assume that the short-term nominal interest rate is constant and equal to i> 0. Here, we'll be thinking about one time period as being one year, so this interest rate is annual. Suppose that you buy a ten-year discount bond (or zero-coupon bond) in 2018; when it matures in 2028, the bond has a face value of F dollars. i. What's the present value of the bond's payout? ii. Now, suppose you hold on to the bond until 2019 and re-calculate the present value. What's the present value of the same bond, as computed in 2019? Is this greater than, less than, or equal to the present value you computed in 2018? ii. What's the present value of the same bond in 2028, the day that the face value is redeemed for cash? What, in general, is the relationship between the present value of a discount bond and it's time to maturity? iv. Assume that, at each date, the bond's price is equal to its present value. Does the price go up, down, or remain the same between 2018 and 2028? Does the yield to maturity go up, down, or remain the same between 2018 and 2028? (b) Now, suppose that you buy a consol (or perpetuity) in 2018 that promises a coupon payment of i. What is the present value of the consol's stream of payouts, as computed in 2018? In 2019? ii. Does the consol have a maturity date? How do you reconcile your answer to 1.a.ii. with your C each year. Again, assume that interest rates are constant and equal to i. Does the present value go up, down, or remain the same over time? answer to 1.b.i