Bond A pays $8,000 in 20 years. Bond B pays $8,000 in 40 years. (To keep things
ID: 1239416 • Letter: B
Question
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 bond
holder 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:
Explanation / Answer
a.PV of bond A= 8000/1.035^20=$4020.527 PV of bond B= 8000/1.035^40=$2020.58 Since the present value of bond A is more, bond A is worth more. b.If the interest rate increases to 7 percent PV of bond A= $2067.35 PV of bond B= $534.24 bond B has a larger percentage change in value= 73.56% decrease bond A decreases by 48.58% c.The value of a bond [falls] when the interest rate increases, and bonds with a longer time to maturity are [more] sensitive to changes in the interest rate.