If the expected inflation rate is 5% and the real interest rate is 2.86% what is the mortgage rate that the homeowner needs to pay at, using the appropriate interest rate formula

To calculate the mortgage rate (also known as the nominal interest rate) that the homeowner needs to pay, you can use the **Fisher equation**, which relates the nominal interest rate, the real interest rate, and the inflation rate. The formula is:

\[
1 + i = (1 + r) \times (1 + \pi)
\]

Where:
- \( i \) is the nominal interest rate (mortgage rate),
- \( r \) is the real interest rate,
- \( \pi \) is the expected inflation rate.

Given:
- Expected inflation rate \( \pi = 5\% = 0.05 \)
- Real interest rate \( r = 2.86\% = 0.0286 \)

We need to solve for \( i \):

\[
1 + i = (1 + 0.0286) \times (1 + 0.05)
\]

\[
1 + i = 1.0286 \times 1.05
\]

\[
1 + i = 1.08003
\]

\[
i = 1.08003 - 1 = 0.08003
\]

\[
i = 8.003\%
\]

So, the nominal interest rate (mortgage rate) that the homeowner needs to pay is **8.003%**.

Would you like more details on this calculation or have any further questions?

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Here are some related questions you might be interested in:

1. What is the difference between nominal and real interest rates?
2. How does inflation affect mortgage rates?
3. Can the Fisher equation be used for long-term interest rate predictions?
4. What happens to mortgage rates if inflation unexpectedly increases?
5. What are the implications of negative real interest rates on borrowing?
6. How do central banks influence real and nominal interest rates?
7. What are other methods for calculating interest rates in different economic contexts?
8. How does inflation expectation differ from actual inflation in economic models?

**Tip:** When dealing with financial formulas, always ensure the consistency of the rate periods (e.g., annual rates) and the units (e.g., percentages).

Learn how to calculate the mortgage rate using the Fisher equation with real and expected inflation rates. Solve for the nominal interest rate with detailed steps. Given inflation rate of 5% and real interest rate of 2.86%, find the mortgage rate needed by homeowners.

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