An annual$-$coupon corporate bond is priced to yield a $7\%$ annual effective rate. It has a price of $940\mathrm{.}29$ and a Macaulay duration of $6\mathrm{.}5317.$ Estimate the change in price if the bond's yield to maturity increases by $0\mathrm{.}10\%,$ using:

$($a$)$ the first$-$order Macaulay approximation

$($b$)$ the first$-$order modified approximation