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To solve the problem in the image, we are tasked with calculating the effective annual rate of interest \( i \). The given information includes the following:

- Cash flow today (Year 0): 100
- Cash flow in 1 year: 200
- Cash flow in 2 years: 100
- Present value (PV) of the cash flows: 364.46
- We need to find \( i \), the effective annual rate of interest.

### Formula for Present Value:

The present value of future cash flows can be calculated using the formula:

\[
PV = \frac{C_0}{(1 + i)^0} + \frac{C_1}{(1 + i)^1} + \frac{C_2}{(1 + i)^2}
\]

Where:
- \( PV = 364.46 \)
- \( C_0 = 100 \) (cash flow today)
- \( C_1 = 200 \) (cash flow in one year)
- \( C_2 = 100 \) (cash flow in two years)

Substituting the values into the formula:

\[
364.46 = 100 + \frac{200}{(1 + i)} + \frac{100}{(1 + i)^2}
\]

Now, let's solve for \( i \). I'll calculate this step by step.The effective annual interest rate \( i \) is approximately 0.100, or 10%.

Thus, the correct answer is **A: 10%**.

Would you like further details or clarifications on any step of this solution?

Here are 5 related questions you might find helpful:
1. How is the present value of future cash flows calculated in different scenarios?
2. What is the difference between effective annual interest rates and nominal rates?
3. How does changing the timing of cash flows affect the present value?
4. Can you explain the process of solving non-linear equations like this one?
5. How can interest rates be applied to various financial instruments?

**Tip:** When dealing with cash flows and interest rates, always be mindful of whether you're using nominal or effective interest rates, as they yield different present values.

Mike receives cash flows of 100 today, 200 in one year, and 100 in two years. The present value of these cash flows is 364.46 at an annual effective rate of interest i. Calculate i.

Learn how to calculate the effective interest rate given a set of cash flows (100 today, 200 in one year, 100 in two years) and a present value of 364.46. Detailed step-by-step solution covering the present value formula and time value of money principles.

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