Intermediate Microeconomics and Its Application 12th Edition by Walter Nicholson,Christopher Snyder

Exercise 5

make use of the material on compound interest that is in the appendix to this chapter.
Although perpetual bonds are illegal in the United States, sometimes it is easiest to assume that interest payments last forever to show some simple results based on Equation 14A.24. Use that equation to show the following:
a. Assuming no inflation, the value of a bond that pays $10 per year is $200 with a real rate of interest of 5 percent.
b. If inflation is 3 percent per year and interest payments rise at that rate, the current value of the perpetual bond is still $200.
c. If inflation is 3 percent per year and the bond's payments are fixed at $10, that the current value of the perpetual bond is $125 can be shown in two ways:
i. By assuming that the nominal rate of interest is 8 percent and using that rate for discounting
ii. By adjusting the $10 payment for inflation in each period and using a real discount rate of 5 percent (Hint: This latter proof is easiest if