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, calculate the bond's semiannual coupon rate:

$40 semiannual interest / $1,000 par value = 0.04 or 4% semiannual coupon rate

Using the formula for the present value of a bond with semiannual payments, we can calculate the bond's present value:

PV = ($40 / 0.10) x [1 - 1 / (1 + 0.10 / 2)^(20 x 2)] + ($1,000 / (1 + 0.10 / 2)^(20 x 2))

PV = $400 x [1 - 1 / (1.05)^40] + $1,000 / (1.05)^40

PV = $828

Therefore, Mary should be willing to pay approximately $828 for the bond. Choice D is the closest option to this value.

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