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 $2\mathrm{.}91\%$ p$.$a$.$ compounded half$-$yearly $($j$2=2\mathrm{.}91\%$ 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 $10$Answer

a$.$

$128305\mathrm{.}19$

b$.$

$127797\mathrm{.}27$

c$.$

$126796\mathrm{.}89$

d$.$

$63437\mathrm{.}13$