Here$$s an example of how breakpoint discounts on sales commissions for mutual fund investors work:

Sales charge

Less than $$25,000,5\mathrm{.}25\%$

$$25,000$ to $$49,999,5\%$

$$50,000$ to $99,999,4\mathrm{.}25\%$

$$100,000$ to $$249,999,3\mathrm{.}25\%$

Nancy Dolan is interested in the T Rowe Price Mid Cap Fund. Assume the NAV is $19\mathrm{.}21.$

a$.$ What minimum amount of shares must Nancy purchase to have a sales charge of $5\%?($Round up to the nearest share even if it is less than $5.)$

b$.$ What minimum amount of shares must Nancy purchase to have a sales charge of $4\mathrm{.}25\%?($Round up to the nearest share even if it is less than $5.)$