Question 1: (16 marks) A 15-year annuity pays $1,500 per month, and payments are made at the end of each month. If the interest rate is 13 percent compounded monthly for the first seven years, and 10 percent compounded monthly thereafter, what is the present value of the annuity? Question 2: (12 marks) Adam won $17 million in a lottery. a) If Adam decided to invest the entire $17 million to fund scholarships at his Alma Mater forever, how much could he provide annually if the interest rate on the investment was 5% (compounded annually) and scholarships are paid at the beginning of the year? b) If Adam could invest the funds at 5% compounded quarterly, what is the total amount of annual scholarships that could be provided at the beginning of each year? c) If Adam instead invested the funds for 2 years at 5% compounded quarterly, then established the scholarship fund, what is the total amount of annual scholarships that could be provided beginning in 2 years? (Scholarships are provided at the beginning of each year). Question 3: (15 marks) Kelsey and Blake are thinking of purchasing a house. The house costs $320,000 and they have saved $80,000 as a down payment. The rest will be secured by a mortgage. The bank is offering a 25-year mortgage with a term of 5 years at a rate of 7% (APR) requiring monthly payments. a) Calculate the amount of each payment. b) Calculate the monthly payments if they are made at the beginning of the month rather than the end c) If Kelsey and Blake can only afford to pay $1,500 each month, how much would the bank allow them to borrow? (These payments are made at the end of each month) d) Assuming they secure the mortgage in part (c), how much of the 81'st mortgage payment is principal and how much is interest