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 bondholder receives.)

Required:
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?

Answer 1

$4020.53

$2020.58

The bond that pays $8000 in 20 years because its present value is higher

$2067.35

$534.24

The bond that pays $8000 in 40 years

Step-by-step explanation:

formula for finding present value

pv = fv / (1 + r)^n

FV = Future value

P = Present value

R = interest rate

N = number of years

a. $8000 / (1.035)^20 = $4020.53

$8000 / (1.035)^40 = $2020.58

b. $8000 / (1.07)^20 = $2067.35

$8000 / (1.07)^40 = $534.24

There is a 73.5% decrease in the price of the bond that pays $8000 in 40 years

There is a 48.6% decrease in the price of the bond that pays $8000 in 20 years