Question

A college wants to provide students with a perpetual scholarship of $10,000 at the end of every 3 months. How large should their endowment fund be if invested at X% (choose the rate) compounded quarterly?

Answer 1

To provide a perpetual scholarship of $10,000 every 3 months with a 7% interest rate compounded quarterly, the college would need an endowment fund of approximately $571,428.57.

Step-by-step explanation:

Calculating the Perpetual Scholarship Endowment

To calculate the endowment fund necessary for a perpetual scholarship of $10,000 every 3 months, we need to determine the present value of a perpetuity. Let's assume the fund is invested at a 7% annual interest rate, compounded quarterly. The formula for the present value of a perpetuity is PV = PMT / r, where PMT is the periodic payment and r is the periodic interest rate.

First, convert the annual interest rate to a quarterly interest rate: r = 7% / 4 = 0.0175 per quarter. Then, using the perpetuity formula: Endowment Fund = $10,000 / 0.0175 = $571,428.57. Hence, the college would need an endowment of approximately $571,428.57.

This calculation is based on the assumption that the 7% interest rate is maintained and compounds quarterly without any withdrawals other than the scholarship payments.