1. An engineer planning for her retirement is considering a zero-coupon bond which has a face value of $50,000 and a maturity date 20 years from now. If she buys the bond she plans on holding it to maturity. How much should she pay for the bond if her alternative investment pays a 5% nominal annual interest compounded quarterly? Ignore the impacts of taxation.
2. A 30-year loan of 1,000 is repaid with payments at the end of each year. Each of the first ten payments equals the amount of interest due. Each of the next ten payments equals 150% of the amount of interst due. Each of the last ten payments is X. The lender charges interest at an annual effective rate of 10%. Calculate X.