A person buys a five$-$year, $$1,000$ certificate of deposit that carries a nominal rate of $9$ percent, compounded semiannually. Six months after this purchase, a $\frac{41}{2}-$year $CD$ at the same bank offers a $9\mathrm{.}5$ percent annual rate, also compounded semiannually. How much difference is there in total interest paid by the two competing investments?