A corporate bond with a $1,000 face value pays a $50 coupon every six months. The bond will mature in ten years, and has a nominal yield to maturity of 9 percent. What is the price of the bond?

Question

Quizplus · Accepted Answer

We can use the formula for present value of a bond:

PV = (C / (1 + r/2)^n) + (C / (1 + r/2)^(n-1)) + ... + (C + FV / (1 + r/2)^(n-1))

Where PV is the present value, C is the coupon payment, r is the nominal yield to maturity, n is the number of periods (in this case 20 since there are 10 years and two coupon payments per year), and FV is the face value.

Plugging in the numbers:

PV = (50 / (1 + 0.09/2)^20) + (50 / (1 + 0.09/2)^19) + ... + (50 + 1000 / (1 + 0.09/2)^19)

PV = 50 x (1 - 1/(1 + 0.09/2)^20) / (0.09/2) + 1000 / (1 + 0.09/2)^20

PV = $1,065.04

A Corporate Bond with a $1,000 Face Value Pays a $50