Mary wants to purchase a 20-year bond that has a par value of $1,000 and makes semiannual interest payments of $40. If her required yield to maturity is 10%, which of the following is closest to how much should Mary be willing to pay for the bond?

Question

Quizplus · Accepted Answer

First, we need to calculate the total number of coupon payments made over the life of the bond, which is 20 years x 2 payments per year = 40 payments.

Next, we can calculate the present value of the bond's cash flows using the formula:
PV = (C / r) x (1 - 1 / (1 + r)^n) + F / (1 + r)^n
where:
PV = present value of the bond
C = semiannual coupon payment ($40)
r = required yield to maturity (10% / 2 = 5% per semiannual period)
n = total number of semiannual periods (40)
F = par value of the bond ($1,000)

Plugging in these values, we get:
PV = (40 / 0.05) x (1 - 1 / 1.05^40) + 1000 / 1.05^40
PV = 790.79 + 37.68
PV = $828.47

Therefore, Mary should be willing to pay about $828 for the bond, which is closest to answer choice D.

Mary Wants to Purchase a 20-Year Bond That Has a Par