$10.$ 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 $3\mathrm{.}6\%$ p$.$a$.$ compounded half$-$yearly $($j$2=3\mathrm{.}6\%$ 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$\mathrm{.}159997\mathrm{.}74$

b$\mathrm{.}161587\mathrm{.}10$

c$\mathrm{.}80072\mathrm{.}90$

d$\mathrm{.}162397\mathrm{.}17$

$11.$ Today is $1/7/2021,$ John plans to deposit $$500$ at the beginning of each month into an investment fund. The first deposit will be deposited today. John predicts that the return rate of this fund will be j$2=3\mathrm{.}68\%$ from $1/7/2021$ to $30/9/2021$ and j$2=2\mathrm{.}38\%$ from $1/10/2021$ to $31/12/2021.$ What will be balance amount of this account on $31/12/2021?$ Round your answer to three decimal places.

Question $11$Answer

a$\mathrm{.}3025\mathrm{.}390$

b$\mathrm{.}3024\mathrm{.}030$

c$\mathrm{.}3024\mathrm{.}174$

d$\mathrm{.}3023\mathrm{.}509$