question 22 (1 point)\nnow consider a 4% annual coupon bond with a face value of $1000, a yield to maturity…

question 22 (1 point)\nnow consider a 4% annual coupon bond with a face value of $1000, a yield to maturity of 6% and ten years to maturity.\nii) using the formula below calculate the price of the ten - year bond\n$p = \\frac{c}{i}(1 - \\frac{1}{(1 + i)^n})+\\frac{f}{(1 + i)^n}$

question 22 (1 point)\nnow consider a 4% annual coupon bond with a face value of $1000, a yield to maturity of 6% and ten years to maturity.\nii) using the formula below calculate the price of the ten - year bond\n$p = \\frac{c}{i}(1 - \\frac{1}{(1 + i)^n})+\\frac{f}{(1 + i)^n}$

Answer

Explanation:

Step1: Identify the values

The annual coupon rate is 4%, so the annual coupon payment $C = 0.04\times1000=40$. The face - value $F = 1000$, the yield to maturity $i=0.06$, and the number of years to maturity $n = 10$.

Step2: Calculate the present - value of the coupon payments

First, calculate the present - value of the coupon payments part of the formula: $\frac{C}{i}(1-\frac{1}{(1 + i)^n})=\frac{40}{0.06}(1-\frac{1}{(1 + 0.06)^{10}})$. We know that $(1 + 0.06)^{10}\approx1.7908477$. Then $\frac{1}{(1 + 0.06)^{10}}\approx0.5583948$. And $1-\frac{1}{(1 + 0.06)^{10}}\approx1 - 0.5583948=0.4416052$. $\frac{40}{0.06}(1-\frac{1}{(1 + 0.06)^{10}})=\frac{40}{0.06}\times0.4416052\approx40\times7.333333\times0.4416052\approx130.1079$.

Step3: Calculate the present - value of the face - value

Next, calculate the present - value of the face - value part of the formula: $\frac{F}{(1 + i)^n}=\frac{1000}{(1 + 0.06)^{10}}\approx1000\times0.5583948 = 558.3948$.

Step4: Calculate the bond price

Finally, add the two parts together: $P=\frac{C}{i}(1-\frac{1}{(1 + i)^n})+\frac{F}{(1 + i)^n}\approx130.1079+558.3948 = 852.8027\approx852.80$.

Answer:

$852.80$