Assume that you own a $$1$million par value corporate bond that pays $7\%$ in coupon interest $(3\mathrm{.}5\%$ semiannual$),$ has $4$ years remaining to maturity, and is immediately callable at par. Its current market yield is $7\%$ and it is priced at par. If rates on comparable securities fall by more than $40$ basis points $(0\mathrm{.}2\%$ semiannually$),$ the bond will be called$($a$)$Calculate the bonds price if the market rate increases by $50$ basis points $(0\mathrm{.}25\%$ semiannually$)$ using the present value formula from$($b$)$Calculate the bonds effective duration assuming a $50$ basis$-$point increase or decrease in market rates