Suppose that a wealthy UCD graduate decides to make an annual gift to fund undergraduate scholarships for ME majors. The first of these gifts will be given today and it is anticipated that the gifts will continue forever. The nominal discount rate is 8% and the rate of inflation is 2%.
a.) What is the present value of the graduate's gift if it totals $10,000 per year in real terms?
b.) The ARE department anticipates that, in each of the next 50 years, it can recruit one extra graduate to start a perpetual gift of $10,000 per year in real terms, i.e., this year the department receives one $10,000 gift, next 50 year it receives two such gifts, the next year three gifts and so on.
After year 50, no new donors are recruited, so the department receives 51 gifts per year from the existing donors. What is the present value of all of the scholarship gifts that the department anticipates receiving?