Assume that you wish to purchase a 20-year bond that has a maturity value of $1,000 and a coupon interest rate of 8%,paid semiannually.If you require a 10% rate of return on this investment,what is the maximum price that you would be willing to pay for this bond?

Question

Quizplus · Accepted Answer

Firstly, let's calculate the coupon payment:
Coupon rate = 8%
Maturity value = $1,000
Coupon payment = Coupon rate x Maturity value / Number of payments per year
Coupon payment = 8% x $1,000 / 2
Coupon payment = $40

Now, we can use the formula for the present value of a bond:
PV = Coupon payment x [1 - 1/(1+r)^n]/r + Maturity value/(1+r)^n

Where:
r = semiannual discount rate = 10%/2 = 5%
n = number of semiannual periods = 20 years x 2 = 40 periods

PV = $40 x [1 - 1/(1+5%)^40]/5% + $1,000/(1+5%)^40
PV = $828.29

Therefore, the maximum price that you should be willing to pay for this bond is $828.29, which is choice D.

Assume That You Wish to Purchase a 20-Year Bond That