Question / a) You would like to travel in 5 years from now, and you can save $3,100 per year, beginning one year from today. You plan to deposit the funds in a mutual fund that you think will return 8.5% per year. Under these conditions, how much would you have just after you make the 5th deposit, 5 years from now? (5 marks) b) Your friend offers to pay you an annuity of $2,500 at the end of each year for 3 years in return for cash today. You could earn 5.5% on your money in other investments with equal risk. What is the most you should pay for the annuity? (5 marks) c) What annual payment must you receive in order to earn a 6.5% rate of return on a perpetuity that has a cost of $1,250? (5 marks) d) Suppose you borrowed $15,000 at a rate of 8.5% and must repay it in 5 equal installments at the end of each of the next 5 years. How much would you still owe at the end of the first year, after you have made the first payment? (5 marks) e) Your 75-year-old grandmother expects to live for another 15 years. She currently has $1,000,000 of savings, which is invested to earn a guaranteed 5% rate of return. If inflation averages 2% per year, how much can she withdraw (to the nearest dollar) at the beginning of each year and keep the withdrawals constant in real terms, i.e., growing at the same rate as inflation and thus enabling her to maintain a constant standard of living? (10 marks)