The duration of an $11-$year, $$1,000$ Treasury bond paying a $10$ percent semiannual coupon and selling at par has been estimated at $6\mathrm{.}9106$ years. a$.$ What is the modified duration of the bond? What is the dollar duration of the bond? b$.$ What will be the estimated price change on the bond if interest rates increase $0\mathrm{.}10$ percent $(10$ basis points$)?$ If rates decrease $0\mathrm{.}20$ percent $(20$ basis points$)?$ c$.$ What would the actual price of the bond be under each rate change situation in part $($b$)$ using the traditional present value bond pricing techniques? What is the amount of error in each case?