(a) A scholarship is set up that makes two payments a year. The first payment is $750 and the second payment, made exactly 6 months later, is $1500. This payment scheme continues forever. If money can be invested at j1 = 9%, how much money is needed to fund this scholarship six months before the first payment is to be made?

(b) Another university sets up two scholarship funds. The first one pays out $1200 a year, starting one year from now. The second one pays out $100 in the first year, $200 in the second year, $300 in the third year, and so on. At what interest rate would the present value of the two scholarships be the same? (For BONUS marks: At what interest rate would the difference between the present value of the two scholarship funds be maximized?)