Today you have decided to endow the Dahiya-Pinkowitz Chair for Excellence in Finance (hint, hint…).  You want the chair to provide an annual payment of 47,571 every year forever, with the first payment starting exactly 11 years from today.  Endowments at Georgetown earn a rate of 0.05 (APR), compounded annually, and that rate is never going to change.  In order to ensure the Chair is able to make the annual payments, how much money do you need to donate TODAY?

To solve this problem, we need to determine how much money you need to donate **today** to endow a chair that provides an annual payment of \$47,571, with the first payment starting 11 years from today. The endowment earns an annual interest rate of 5% (APR), compounded annually.

We will solve this problem in two parts:

### Step 1: Present value of the perpetuity
A perpetuity is a stream of cash flows that continues indefinitely. The formula for the present value $ PV $ of a perpetuity that starts paying in the future is:

\[
PV_{\text{perpetuity}} = \frac{C}{r}
\]

Where:
- $ C = 47,571 $ (the annual payment),
- $ r = 0.05 $ (the interest rate).

\[
PV_{\text{perpetuity}} = \frac{47,571}{0.05} = 951,420
\]

This amount, \$951,420, represents the present value of the perpetuity **at year 11**, which is when the first payment is made.

### Step 2: Discounting the value back to today
Since the endowment begins paying in 11 years, we now need to discount this \$951,420 back to today's value using the formula for the present value of a lump sum:

\[
PV_{\text{today}} = \frac{PV_{\text{perpetuity}}}{(1 + r)^t}
\]

Where:
- $ PV_{\text{perpetuity}} = 951,420 $,
- $ r = 0.05 $,
- $ t = 11 $ (the number of years until the first payment).

Let's calculate the present value today.The amount you need to donate **today** to endow the Dahiya-Pinkowitz Chair for Excellence in Finance is approximately **\$556,275.57**.

Would you like further clarification on any part of this process?

Here are five related questions:
1. How would the donation amount change if the interest rate was different?
2. What if the payments started 15 years from today instead of 11?
3. How would the donation amount be affected if the chair provided increasing payments each year?
4. What happens if the interest rate is compounded more frequently than annually?
5. How is this problem similar to or different from calculating the value of a bond?

**Tip**: When discounting future cash flows, earlier cash flows are worth more than later ones due to the time value of money.

Today you have decided to endow the Dahiya-Pinkowitz Chair for Excellence in Finance (hint, hint…). You want the chair to provide an annual payment of 47,571 every year forever, with the first payment starting exactly 11 years from today. Endowments at Georgetown earn a rate of 0.05 (APR), compounded annually, and that rate is never going to change. In order to ensure the Chair is able to make the annual payments, how much money do you need to donate TODAY?

Learn how to calculate the present value of an endowment that pays $47,571 annually starting 11 years from today. Understand key concepts like perpetuity and discounting with a 5% APR compounded annually. Ideal for college-level finance students.

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