An alumnus has given Michigan State University \(\$ 10\) million to build and operate a laboratory. Annual operating cost is estimated to be \(\$ 100,000\). The endowment will earn 6 percent interest. Assume an infinite life for the laboratory and determine how much money may be used for its construction. a) \(\$ 5.00 \times 10^{6}\) c) \(\$ 8.72 \times 10^{6}\) b) \(\$ 8.333106\) d) \(\$ 9.90 \times 10^{6}\)

Educational finance encompasses the methods by which schools, universities, and other educational institutions secure and manage their funds. This finance ensures that there are sufficient resources for the construction of new facilities, like laboratories, as well as for their operation. An endowment fund is a common financial instrument used in the sector.

An endowment is a donation of money or property to a non-profit organization, which uses the earning from the investment of this donation for its ongoing support. In our example, Michigan State University received a \( 10\) million endowment meant to build and sustain a laboratory. Proper management of these funds is crucial to ensure the lab's long-term feasibility without depleting the principal of the endowment. Understanding the constraints, such as only spending the earned interest and not the principal, allows managers to make informed decisions about construction budgets and operational expenditures.

Interest rate calculations are fundamental to managing an endowment fund. In our case, the university's \( 10\) million endowment earns interest, which is the key to financing the lab's operating costs.

The interest rate, in this situation 6%, determines how much income the fund generates annually. Calculating this is straightforward: multiply the endowment's total principal by the interest rate. For instance, \(10,000,000 \times 0.06 = \$ 600,000\), which is the annual interest amount available for the lab's expenses.

The concept of 'infinite life' in financial terms means that the fund should exist indefinitely, without reducing its principal. The calculated interest has to be sufficient to cover annual expenses while preserving the original endowment amount. By analyzing interest rates and their implications, educational institutions can balance their budgets and secure financial sustainability for their programs and facilities.

Operating costs for educational facilities refer to the ongoing expenses necessary for their daily function and upkeep. Such costs include utilities, maintenance, staff salaries, and equipment. In our problem, the laboratory's operating costs are estimated to be \( 100,000\) annually.

When managing an endowment fund, it's important to ensure that the annual operating costs do not exceed the yearly interest generated. This ensures that the educational facility can continue to operate indefinitely without eating into the initial capital. The proper management of these costs is vital; it requires prudent financial planning and regular reviews of expenses and income. By securing a stable funding stream through interest earnings, educational institutions can focus on delivering quality education and research without the worry of financial shortfalls.