A wealthy benefactor just donated some money to the local college. This gift was established to provide scholarships for worthy students. The first scholarships will be granted one year from now for a total of $35,000. Annually thereafter, the scholarship amount will be increased by 5.5 percent to help offset the effects of inflation. The scholarship fund will last indefinitely. What is the value of this gift today at a discount rate of 8 percent?

Question

Quizplus · Accepted Answer

The value of the scholarship fund today can be calculated using the perpetuity formula, which is:

Present value = Annual amount / Discount rate

To use this formula, we need to calculate the first year's scholarship amount, which is $35,000. Then, we can use the given annual increase rate of 5.5% to calculate the scholarship amount in all subsequent years.

Next, we need the discount rate, which is 8%.

Putting it all together, we get:

Present value = $35,000 / (0.08 - 0.055) = $35,000 / 0.025 = $1,400,000

Therefore, the value of the gift today is $1,400,000, which is option D.

A Wealthy Benefactor Just Donated Some Money to the Local