In this problem, we are given the following parameters:

• Nominal interest rate: 5.5% compounded annually.
• Inflation rates: First, 2% and then 8%.

We are asked to identify the nominal interest rate (i), the future value factor (f), and the real interest rate (i') for both cases.

Let's break this down:

Case 1: Inflation = 2%

1. Nominal Interest Rate (i)

This is the rate the bank is offering, which is 5.5% compounded annually.

$i = 5.5\% = 0.055$

2. Future Value Factor (f)

The future value factor is given by:

$f = (1 + i) = (1 + 0.055) = 1.055$

3. Real Interest Rate (i')

To calculate the real interest rate, we use the formula:

$i' = \frac{1 + i}{1 + \text{inflation rate}} - 1$

Substituting the given inflation rate of 2% (or 0.02):

$i' = \frac{1 + 0.055}{1 + 0.02} - 1 = \frac{1.055}{1.02} - 1 \approx 0.0343 \text{ or } 3.43\%$

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Case 2: Inflation = 8%

1. Nominal Interest Rate (i)

The nominal interest rate remains the same as before, 5.5% compounded annually.

$i = 5.5\% = 0.055$

2. Future Value Factor (f)

The future value factor remains the same as well:

$f = (1 + i) = (1 + 0.055) = 1.055$

3. Real Interest Rate (i')

Using the formula again, but now for 8% inflation (or 0.08):

$i' = \frac{1 + 0.055}{1 + 0.08} - 1 = \frac{1.055}{1.08} - 1 \approx -0.0231 \text{ or } -2.31\%$

Summary:

When inflation is 2%:

• i = 5.5%
• f = 1.055
• i' ≈ 3.43%

When inflation is 8%:

• i = 5.5%
• f = 1.055
• i' ≈ -2.31%

Would you like further clarification or additional details on any of the steps involved?

Here are 5 related questions for deeper understanding:

1. How would the real interest rate change if the nominal interest rate increased to 6%?
2. What would happen to the future value factor if the interest were compounded monthly instead of annually?
3. How do inflation expectations affect the real return on investment?
4. Can you calculate the real interest rate for a negative nominal interest rate (e.g., -1%)?
5. How can the Fisher equation be used to estimate the real interest rate more precisely?

Tip: To understand the impact of inflation, always compare nominal rates with real rates, as inflation erodes purchasing power over time.