Bond A pays $8,000 in 20 years. Bond B pays $8,000 in 40 years. (To keep things simple, assume that these are zero-coupon bonds, meaning 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.”