Personal Finance Problem

P$5-27$ Creating an endowment On completion of her introductory finance course, Marla Lee was so pleased with the amount of useful and interesting knowledge she gained that she convinced her parents, who were wealthy alumni of the university she was attending, to create an endowment. The endowment is to allow three needy students to take the introductory finance course each year in perpetuity. The guaranteed annual cost of tuition and books for the course is $$600$ per student. The endowment will be created by making a single payment to the university. The university expects to earn exactly $6\%$ per year on these funds.

a$.$ How large an initial single payment must Marla's parents make to the university to fund the endowment?

b$.$ What amount would be needed to fund the endowment if the university could earn $9\%$ rather than $6\%$ per year on the funds?