An alumnus sets up a scholarship at her university with a $10,000 donation.The annual scholarship will $R,with the first payment made today.What is R,if the money can be invested at j₁ = 11%? (Answer to nearest dollar)

Question

Quizplus · Accepted Answer

We can use the formula for present value of an annuity to find the value of R:

PV = R * [1 - (1 + j)^(-n)] / j

where PV is the present value of the scholarship (which is equal to the initial donation of $10,000), j is the annual interest rate (11% or 0.11), and n is the number of payments (which is infinite, since the scholarship is ongoing).

Therefore:

$10,000 = R * [1 - (1 + 0.11)^(-∞)] / 0.11
$10,000 = R * [1 - 0] / 0.11
$10,000 = R * 9.090909...

R = $10,000 / 9.090909...
R = $1,099.99 (rounded to nearest dollar)

So the annual scholarship amount is $1,100, which is closest to option B.

An Alumnus Sets Up a Scholarship at Her University with a $10,000