Mike wants to donate $$5,000,000$ to establish a fund to provide an annual scholarship in perpetuity. The fund will earn an interest rate of $5\mathrm{.}26\%$ p$.$a$.$ compounded half$-$yearly $($j$2=5\mathrm{.}26\%$ p$.$a$.)$ and the first scholarship will be first awarded $3\mathrm{.}5$ years after the date of the donation.

$($b$)$ Assume that two years after the donation, Mike needs to withdraw $$1,000,000$ from the fund and use the remaining amount to provide an annual scholarship in perpetuity. The time of the first scholarship will be unchanged $(3\mathrm{.}5$ years after the date of the donation$).$ What is the new annual scholarship amount $($rounded to two decimal places$)?$

Question $10$

a$\mathrm{.}122734\mathrm{.}37$

b$\mathrm{.}250601\mathrm{.}30$

c$\mathrm{.}244995\mathrm{.}09$

d$\mathrm{.}248696\mathrm{.}65$