You are interviewing for an internship with an investment firm. They ask you to come up with the price to charge on a security that makes growing annual payments for 10 years. The first payment is one year from today in the amount of $100 and it grows at 2% per year. The investment firm thinks potential investors have a required return of 9% per year. What is the highest price investors would be willing to pay for this security?

To calculate the highest price an investor would be willing to pay for a security that makes growing annual payments over a set period, we can use the **present value of a growing annuity formula**. This is appropriate when the cash flows (payments) grow at a constant rate and there is a required rate of return.

The formula for the present value of a growing annuity is:

\[
PV = \frac{C}{r - g} \left(1 - \left(\frac{1 + g}{1 + r}\right)^n \right)
\]

Where:
- $ PV $ = Present value (the price the investors are willing to pay)
- $ C $ = Initial payment (the payment made at the end of the first year), which is $100
- $ r $ = Required return (the discount rate), which is 9% or 0.09
- $ g $ = Growth rate of the payments, which is 2% or 0.02
- $ n $ = Number of periods (years), which is 10

Let me calculate this for you.The highest price investors would be willing to pay for this security is approximately **$692.98**.

Would you like any further details or explanations?

Here are some related questions to think about:
1. How would the price change if the growth rate of the payments increased?
2. What would happen if the required return increased to 12%?
3. How does the duration (number of years) of payments impact the price?
4. How would you calculate the price if the payments didn't grow but remained constant?
5. What if the payments were made continuously rather than annually?

**Tip:** When calculating present values, ensure the growth rate is less than the required return, or the formula will not work as expected.

Calculate the present value of a security with growing annual payments over 10 years, starting at $100 and growing at 2% per year. Learn how the required return of 9% impacts the highest price investors are willing to pay, with detailed explanations of the present value of a growing annuity formula. Suitable for finance students.

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