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 4.19% p.a. compounded half-yearly (j₂=4.19% p.a.) and the first scholarship will be first awarded 3.5 years after the date of the donation.

(a) What is the amount of the annual scholarship (rounded to two decimal places)?

(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 (3.5 years after the date of the donation). What is the new annual scholarship amount (rounded to two decimal places)?