This year Aryna Sabalenka of Belarus won her first US Open, beating American Jessica Pegula in straight

sets and collecting a prize of $$3\mathrm{.}6$ million.

a$)$ If Aryna decided to invest all her US Open winnings, into an investment earning $7\mathrm{.}5\%$ compounded

quarterly for the next $5$ years, how much would Aryna have at the end of $5$ years? $(4$ marks$)$

b$)$ After $5$ years, if Aryna uses the accumulated funds from $($a$)$ to donate to her favourite charities, how

much could she donate annually at the end of each year, if she wanted to continue her donations

for $20$ years? $($Assume funds are kept in the same investment$)(6$ marks$)$

c$)$ Referring to $($b$)$ how much could Aryna donate to her favourite charities each year if the donations

were made at the beginning of each year? $($