Q6) (15 marks) a) Define a perpetuity. b) Give the formula for the present value of a perpetuity due that pays $1 per period in terms of the effective interest rate per period r. Xenia wants to fund a wildlife sanctuary. Estimated expenses are $1000 per month. The interest rate is 1.5% compounded quarterly. c) What is the effective monthly rate? d) How much money does she need to buy a perpetuity to fund the sanctuary? e) If the interest rate changes to 3. 0% Compounded quarterly, what is the new value of the perpetuity? f) If she sells the perpetuity and buys an annuity immediate with monthly payments of $2000, how many months will she get if the last payment is a balloon payment