Question

Old Main is a historic campus landmark that needs maintenance and repairs to its bell tower every 15 years. Each time the maintenance and repairs are completed, this costs $850,000. The university is seeking a donor to establish an endowment that will pay for all the Old Main bell tower repair and maintenance costs. How large of a charitable gift should the University pursue, assuming the donor's gift is invested in a fund that earns 4% compounded annually?

Answer 1

The endowment size required to cover the $850,000 maintenance every 15 years, given a 4% compound interest rate, is calculated by determining the present value of a perpetuity adjusted for the 15-year intervals.

Step-by-step explanation:

To determine the size of the endowment needed to cover the $850,000 maintenance and repair costs of the Old Main bell tower every 15 years, we assume the endowment will be invested to yield a 4% compound interest annually. Therefore, we need to find the present value of a perpetuity with $rac{850,000}{(1+0.04)^{15}}$ periodic payments, as the costs are incurred every 15 years, not annually.

The formula for the present value of a perpetuity is PV = P / i, where PV is the present value, P is the periodic payment, and i is the interest rate per period. Using this formula, we calculate:

First, find the periodic payment amount adjusted for 15 years: P = 850,000 / (1.04)^15.

Calculate the present value needed for an endowment: PV = P / 0.04.

Combine the two steps into one formula: PV = 850,000 / (0.04 * (1.04)^15).

Completing these calculations will give the university the size of the endowment needed to establish a fund that covers the bell tower maintenance every 15 years indefinitely.