An insurance company owns a $30-$year $4\mathrm{.}75$ percent Treasury bond. The bond has a $$100,000$ face value and pays its coupon semiannually. Its duration is $16\mathrm{.}7891$ years, current market price is $$107,700$ and its current yield to maturity is $4\mathrm{.}29\%.$ The insurance company is concerned that interest rates may increase by $82$ basis points. Treasury bond futures are currently available with a price of $119\mathrm{.}56.$

If interest rates rise by $82$ basis points, what will be the impact on the insurance company's Treasury bond value? Support your answer with appropriate calculations.

If the insurance company hedges its position in the Treasury bond with a Treasury future, what position should it take in the future? Why?

Suppose interest rates rise by the expected $82$ basis points and the insurance company has hedged its position as you recommend in b$.$ Calculate the net value of the hedge after the increase in interest rates.