A $20-$year, $8\%$ coupon bond is currently priced to have a yield to maturity of $10$ percent. Use the approximation method to answer the following questions:

a$)$ Determine the bond's current price.

b$)$ If the current bond price is $$800,$ determine the rate of return on the bond $($i$.$e$.,$ the holding period yield$)$ if the bond is sold $10$ years later at a price of $$1,200.$

c$)$ If the bond$$s current price is $$800,$ determine the price at which this bond should be sold $5$ years later to earn a holding period yield of $15$ percent.Consider the following bond portfolio:

a$)$ What is the bond portfolio's duration?

b$)$ If the bond portfolio duration is $6\mathrm{.}95$ years, calculate the capital loss on this portfolio

when the yield increases from $10$ to $12$ percent.

c$)$ Suppose the portfolio is immunized over an investment horizon of $6\mathrm{.}95$ years.

Determine the value of the portfolio at the end of this investment horizon.