Question

What is the formula used to calculate the yield to maturity on a 20-year coupon bond with a current yield of 12% and \(1,000 face value that sells for \)2,500

Short answer

The yield to maturity is 3.33%

Step-by-step solution

Step 1. Introduction

A coupon is a payment of interest received by a bondholder from the date of issuance to the bond's maturity date. The "coupon rate," which is computed by summing the total number of coupons paid each year and dividing it by the bond's face value, is the most common way of describing coupons.

Step 2. Explanation

$$\begin{gathered} CouponAmount=CouponRate\times FaceValue \\ =10\%\times 1000 \\ =100 \\ YieldtoMaturity=\frac{Couponamount+\left(\right(Facevalue-sellingprice)/n)}{(Facevalue+sellingprice)/2} \\ =\frac{100+\left(\right(1000-2000)/20)}{(1000+2000)/2} \\ =\frac{100+(-1000/20)}{(3000/2)} \\ =\frac{100-50}{1500} \\ =\frac{50}{1500} \\ =3.33\% \end{gathered}$$