4. (8 points) You're a happy alum of the University of Toronto who would like to endow scholarships for future students. Every year, a scholarship of 10,000 CAD will be given out in your name. The rst scholarship will be given today. To thank you for your generosity, the University will cover the cost of the rst two scholarships. However, you must give them your donation now (not two years from now). in one single payment that will fund the scholarship for the rest of time. (a) Assume the annual interest rate is 3.5%, compounded annually. How much should your donation be? Show your reasoning; use only a scientic calculator. The donation should be at least :| CAD. (b) What happens if the annual interest rate turns out to be lower than planned for? If the annual interest rate is only 3.1% (compounded annually), how many scholarships can be given out before the funds run out, with the initial donation calculated in (9.)? Your count should include the initial two scholarships funded by the university. Show your reasoning; use only a scientic calculator. The scholarship fund will run out after :l scholarships have been given