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

$4\mathrm{.}47\%$ p$.$a$.$ compounded half$-$yearly $(j_2=4\mathrm{.}47\%$ 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$)?$

a$.101959\mathrm{.}37$

b$.206197\mathrm{.}54$

c$.203631\mathrm{.}53$

d$.207511\mathrm{.}86$