A bond with a $1,000 face value and an 8 percent annual coupon pays interest semiannually. The bond will mature in 15 years. The nominal yield to maturity is 11 percent. What is the price of the bond today?

Question

Quizplus · Accepted Answer

First, we need to calculate the number of semiannual periods until maturity, which is 15 years x 2 = 30 semiannual periods.

Next, we need to calculate the semiannual coupon payment, which is $1,000 x 8% / 2 = $40.

Then, we can use the formula for the present value of a bond:

PV = (C / r) x [1 - (1 / (1 + r)^n)] + (F / (1 + r)^n)

where:
PV = present value of the bond
C = semiannual coupon payment
r = nominal yield to maturity / 2
n = number of semiannual periods until maturity
F = face value of the bond

Plugging in the numbers, we get:

PV = ($40 / 0.055) x [1 - (1 / (1 + 0.055)^30)] + ($1,000 / (1 + 0.055)^30)
PV = $781.99

Therefore, the price of the bond today is $781.99. Choice B is the correct answer.

A Bond with a $1,000 Face Value and an 8