Question

You plan to set up an endowment at your alma mater that will fund $240,000 of scholarships each year indefinitely. If the principal (the amount you donate) can be invested at 6.4 percent, compounded annually, how much do you need to donate to the university today, so that the frst scholarships can be awarded beginning one year from now?

Answer 1

To endow $240,000 in annual scholarships with a 6.4% interest rate, donate $3,750,000 today to create a perpetuity that supports the scholarships indefinitely starting in one year.

Step-by-step explanation:

To determine the principal amount needed to donate today to fund $240,000 of scholarships annually at a 6.4 percent interest rate, compounded annually, we use the formula for the present value of a perpetuity. A perpetuity is a type of annuity that lasts indefinitely, in which the first payment is made at the end of the first period. In this case, the first scholarship is to be awarded one year from now.

The present value of a perpetuity is calculated using the formula:

Present Value (PV) = Payment / Interest Rate,

where the Payment is the annual scholarship amount, and the Interest Rate is the annual investment return rate in decimal form.

So, with an annual scholarship of $240,000 and an interest rate of 6.4%, the calculation is:

PV = $240,000 / 0.064 = $3,750,000.

Therefore, you need to donate $3,750,000 to the university today to fund this endowment.