Question

Five years from today, you hope to donate $10,000 to the alumni association. thereafter, you intend for your annual contributions to grow at a rate of 3 percent per year, forever. if you can earn 7 percent per year on your investments, how much must you invest today to fund this donation?

a. $190,724
b. $142,857
c. $222,122
d. $250,000
e. $215,652

Answer 1

Tje correct answer is option a. fund a donation of $10,000 to the alumni association five years from today, and annual contributions growing at a rate of 3 percent per year forever, you need to invest $7,322.78 today.

Step-by-step explanation:

To calculate the amount that must be invested today to fund a future donation, we can use the concept of present value. The present value is the current worth of a future cash flow, taking into account the time value of money. In this case, we want to find the present value of the donation amount after five years, which will then be invested to grow at a rate of 3 percent per year forever.

Using the formula for present value, PV = CF / (1 + r)^n, where PV is the present value, CF is the future cash flow, r is the interest rate, and n is the number of periods, we can calculate the amount that must be invested today as follows:

PV = 10,000 / (1 + 0.07)^5 = $7,322.78

Therefore, the correct option is a. $7,322.78.