After graduating from the University of Adelaide, 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, to create an endowment. The endowment is to allow three needy students to start

their undergraduate studies each year in perpetuity. The guaranteed annual cost of tuition and

books for the course is $6000 per student. The endowment will be created by making a single

payment to the university. The university expects to earn exactly 5.10% per year on these funds.

a. How large an initial single payment must Marlas parents make to the university in one

year to fund the endowment?

b. However, following the Covid-19 pandemic, inflation has surged, leading to a growth

in the prices of books and future tuition fees. If the university estimates that the cost

will rise by 0.5% per year thereafter, how much should they donate now to fund the

endowment?