A corporate bond has $2$ years to maturity, a coupon rate of $3\%,$ a face value of $$1,000$ and pays coupons semiannually. The market interest rate for similar bonds is $0\mathrm{.}045.$ What is the bond's duration? If yields fall by $0\mathrm{.}8$ percentage points, what is the new expected bond price based on its duration $($in $$)?$What is the actual bond price after the change in yields $($in $$)?$What is the difference between the two new bond prices $($in absolute $$)?$