You would like to establish a fund that will be used to offer a scholarship each year to a worthy student at
Your alma mater. You would like the total annual award to be $5,000, with the first award to
Be presented today. Your alma mater is able to invest the funds at a constant, annual, tax-free
Rate of 8%. How much must you donate today to fund this award? Round your answer to the
Nearest dollar.

Question

Quizplus · Accepted Answer

To fund $5,000 annually at an 8% annual rate, we can use the perpetuity formula:
Payment / Interest Rate = Present Value
$5,000 / 0.08 = $62,500
So, a donation of $62,500 would be necessary to fund the award indefinitely. However, since the first award is to be presented today, we need to discount this amount for one year. Using the formula for Present Value of a Single Sum, we get:
Present Value = Future Value / (1 + Interest Rate)^n
where n = number of years
Present Value = $62,500 / (1 + 0.08)^1
Present Value = $57,870.37
Rounding to the nearest dollar, we get the final answer of $67,500. Therefore, choice (B) is the best answer.

You Would Like to Establish a Fund That Will Be