Nancy has built a very profitable business, and she credits the entrepreneurship program at her alma mater for a lot of her success. She would like to donate money to her old school to
Help one worthy graduate each year establish his or her own business. She will donate the
Money today, with the understanding that the first award will go to a graduate of this year's
Freshman class. (That is, the first award will be made four years from now.)Her alma mater is
Able to invest the funds at a constant, annual, tax-free rate of 12%. How much must her
Donation be if she would like for the annual award to be $10,000 a year and wants the program
To continue forever, even after she is no longer around? Round your answer to the nearest
Dollar.

Question

Quizplus · Accepted Answer

Using the perpetuity formula, we can calculate the present value of the donation:
Present Value = Annual Award / Annual Interest Rate
Present Value = $10,000 / 0.12
Present Value = $83,333.33
This means that Nancy would need to donate $83,333.33 today in order to fund an annual award of $10,000 in perpetuity. However, since the first award will only be given four years from now, the present value of the donation would need to grow at the annual interest rate for four years. Using the future value formula, we can calculate the required donation today:
Required Donation Today = Present Value x (1 + Annual Interest Rate)^n
where n is the number of years until the first award is given
Required Donation Today = $83,333.33 x (1 + 0.12)^4
Required Donation Today = $59,315.01
Therefore, Nancy would need to donate $59,315 today to fund an annual award of $10,000 in perpetuity, starting four years from now.

Nancy Has Built a Very Profitable Business, and She Credits