Question

Emma wants to donate $1,000,000 to establish a fund to provide an annual scholarship in perpetuity. The fund will earn an interest rate of j=2.28% p.a. effective and the first scholarship will be first awarded 2.5 years after the date of the donation. (a) What is the amount of the annual scholarship (rounded to two decimal places)?

Answer 1

To find the amount of the annual scholarship, we can use the formula for the present value of a perpetuity. Plugging in the values, the amount of the annual scholarship is approximately $50,634.22.

Step-by-step explanation:

To find the amount of the annual scholarship, we can use the formula for the present value of a perpetuity:

Annual Scholarship = Donation Amount / ((1 + j)^t - 1)

Where:

Donation Amount = $1,000,000 j = 2.28% = 0.0228 (as a decimal) t = 2.5 years

Plugging in the values:

Annual Scholarship = $1,000,000 / ((1 + 0.0228)^2.5 - 1)

Calculating this, the amount of the annual scholarship is approximately $50,634.22 when rounded to two decimal places.