Question

Which \(10,000 bond has the higher yield to maturity, a 20-year bond selling for \)8,000 with a current yield of 20% or a 1-year bond selling for $8,000 with a current yield of 10%?

Short answer

One year bond has higher to maturity.

Step-by-step solution

Step 1. Introduction

Bonds are debt instruments that are issued by governments or businesses to raise funds. Bu purchasign a bond, an invest lends money to the issuer. In return, the investor gets the principal amount along with the interest at the maturity of the bond.

Step 2. Explanation

$$\begin{gathered} CurrentYield=\frac{AnnualCoupon}{Price} \\ 20\%=\frac{AnnualCoupon}{8,000} \\ AnnualCoupon=\$1600 \\ Thebondwillpaycouponof1600peryeartill20years. \\ 8000=\frac{1600}{(1+r)^n} \\ 8000=\frac{1600}{(1+r)^1}+\frac{1600}{(1+r)^2}+\frac{1600}{(1+r)^3}+\frac{1600}{(1+r)^4}+-------+\frac{1600}{(1+r)^20} \\ r=20.13\% \\ 1yearbindselling \\ CurrentYield=\frac{AnnualCoupon}{Price} \\ 10\%=\frac{AnnualCoupon}{8000} \\ AnnualCoupon=800 \\ 80000=\frac{(10,000+800)}{(1+r)} \\ r=35\% \end{gathered}$$