A bank expects to raise $$20$ million in new money if it pays a deposit rate of $7\%.$ It can raise $$60$ million in new money if it pays a deposit rate of $7\mathrm{.}5\%.$ It can raise $$100$ million in new money if it pays a deposit rate of $8\%$ and it can raise $$120$ in new money if it pays a deposit rate of $8\mathrm{.}5\%.$ This bank expects to earn $9\mathrm{.}5\%$ on all money that it receives in new deposits. What is the marginal cost of deposits if this bank raises their deposit rate from $8$ to $8\mathrm{.}5\%?$

$11\%$

$8\mathrm{.}75\%$

$7\mathrm{.}75\%$

$7\%$

$\mathrm{.}5\%$