Bond A pays $\$$8,000 in 20 years. Bond B pays $\$$8,000 in 40 years. (To keep things simple, assume these are zero-coupon bonds, which means the $\$$8,000 is the only payment the bondholder receives.)
a. If the interest rate is 3.5 percent, what is the value of each bond today? Which bond is worth more? Why? ($Hint$: You can use a calculator, but the rule of 70 should make the calculation easy.)
b. If the interest rate increases to 7 percent, what is the value of each bond? Which bond has a larger $percentage$ change in value?
c. Based on the example above, complete the two blanks in this sentence: "The value of a bond
[rises/falls] when the interest rate increases, and bonds with a longer time to maturity are
[more/less] sensitive to changes in the interest rate."