To find the nominal interest rate when given the real interest rate and the inflation rate, we use the Fisher equation:

$(1 + i) = (1 + r)(1 + \pi)$

where:

• $i$ is the nominal interest rate,
• $r$ is the real interest rate,
• $\pi$ is the inflation rate.

Given:

• Real interest rate ($r$) = 5.5% or 0.055
• Inflation rate ($\pi$) = 3.1% or 0.031

Substituting these values into the Fisher equation:

$1 + i = (1 + 0.055)(1 + 0.031)$

First, calculate the right-hand side:

$(1 + 0.055) = 1.055$ $(1 + 0.031) = 1.031$ $1 + i = 1.055 \times 1.031$

Now, perform the multiplication:

$1 + i = 1.088705$

To find the nominal interest rate $i$, subtract 1 from both sides:

$i = 1.088705 - 1$ $i = 0.088705$

Convert the decimal back to a percentage:

$i = 8.8705\%$

Thus, the nominal interest rate is approximately 8.87%.

Would you like more details or have any questions?

Here are five related questions to expand your understanding:

1. How does the Fisher equation help in comparing interest rates in different economic conditions?
2. If the inflation rate increases to 5%, how does that affect the nominal interest rate, assuming the real interest rate remains constant?
3. Can the nominal interest rate ever be lower than the real interest rate? Why or why not?
4. How does a negative inflation rate (deflation) impact the nominal interest rate?
5. What is the impact of hyperinflation on nominal and real interest rates?

Tip: Always express interest rates as decimals (e.g., 5% as 0.05) when using them in formulas to avoid calculation errors.