Assume a $5-$year, $$1,000$ Treasury bond paying a $8$ percent semiannual coupon and selling at par

a$)$ What is the duration for this bond?

b$)$ What is the modified duration of the bond? What is the dollar duration of the bond?

c$)$ Using the duration model, what will be the estimated new price of the bond if interest rates increase $0\mathrm{.}10$ percent $(10$ basis points$)?$ If rates decrease $0\mathrm{.}75$ percent $(75$ basis points$)?$

d$)$ What would the actual price of the bond be under each rate change situation in part $($c$)$ using the traditional present value bond pricing techniques? What is the amount of error in each case?