Subjects finance, algebra

Endowment Calculation

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Search Solutions

Endowment Calculation


1. **Problem Statement:** We want to find the amount of money to donate now (the principal) so that the university can fund a $30,000 annual graduation party forever, starting in one year, with an investment return of 8% per year. 2. **Understanding the Concept:** This is a perpetuity problem. The annual payment (called the perpetuity payment) is $30,000, and the interest rate is 8% or 0.08. 3. **Formula for Perpetuity:** The present value $P$ of a perpetuity paying $A$ each year, starting one year from now, at an interest rate $r$ is: $$ P = \frac{A}{r} $$ 4. **Substitute Values:** Here, $A=30,000$ and $r=0.08$, so: $$ P = \frac{30,000}{0.08} $$ 5. **Calculate:** $$ P = 375,000 $$ 6. **Interpretation:** You need to donate $375,000 now so that the university can invest it at 8% per year and fund a $30,000 annual party forever starting in one year.