use the following information to answer question 21. consider a 4% annual coupon bond with a face value of…

Explanation:

Step1: Identify the values

The face - value $F = 1000$, the annual coupon rate is $4%$, so the annual coupon payment $C=0.04\times1000 = 40$, the yield - to - maturity $i = 0.06$, and the number of years to maturity $n = 5$.

Step2: Calculate the first part of the formula

First, calculate $\frac{C}{i}(1-\frac{1}{(1 + i)^n})$. Substitute the values: $\frac{40}{0.06}(1-\frac{1}{(1 + 0.06)^5})$. $(1 + 0.06)^5=1.06^5\approx1.3382255776$. $\frac{1}{(1 + 0.06)^5}\approx0.7472581728$. $1-\frac{1}{(1 + 0.06)^5}=1 - 0.7472581728 = 0.2527418272$. $\frac{40}{0.06}(1-\frac{1}{(1 + 0.06)^5})=\frac{40}{0.06}\times0.2527418272\approx40\times4.166666667\times0.2527418272\approx42.12363787$.

Step3: Calculate the second part of the formula

Next, calculate $\frac{F}{(1 + i)^n}$. Substitute the values: $\frac{1000}{(1 + 0.06)^5}$. Since $(1 + 0.06)^5\approx1.3382255776$, $\frac{1000}{(1 + 0.06)^5}\approx747.2581728$.

Step4: Calculate the bond price

Add the two parts together: $P=\frac{C}{i}(1-\frac{1}{(1 + i)^n})+\frac{F}{(1 + i)^n}\approx42.12363787+747.2581728\approx889.38$.

Answer:

$889.38$