Suppose the Treasury issued today a four year bond with a notional of $$100$ and a continuously compounded yield of $5\%$ that pays a $4\%$ coupon at the end of each year.

$($a$)$ What is the price of this bond?

$($b$)$ What is the duration of the bond?

$($c$)$ If the yield decreases $10$bps$,$ what should be the approximate change to the price of the bond?

$($d$)$ Suppose that the Federal Reserve just announced a revised monetary policy that causes the Treasury yield curve to change. Discuss the impact of such a change to the yield and price of this bond. Note that a change in the monetary policy may not be reflected in the same way throughout the curve. For example, if the central bank increases the money supply the result is typically a reduction to the short$-$term interest rates.