Frank is lending $1,000 to Sarah for two years. Frank and Sarah agree that Frank should earn a real return of 2 percent per year.

**Instruction:** Enter your responses as whole numbers.

The CPI is 100 at the time that Frank makes the loan. It is expected to be 106 in one year and 112.4 in two years. What nominal rate of interest should Frank charge Sarah?

The nominal rate of interest charged should be 8  Numeric ResponseEdit Unavailable. 8 correct.%.

Suppose Frank and Sarah are unsure about what the CPI will be in two years. How should Frank index Sarah's annual repayments to ensure that he gets an annual 2 percent rate of return?

Frank should charge Sarah 15  Numeric ResponseEdit Unavailable. 15 incorrect.% more than  Correctthe inflation rate.

To determine the nominal interest rate that Frank should charge Sarah, we need to consider the relationship between the **nominal interest rate (i)**, **real interest rate (r)**, and **expected inflation rate (π)**. This relationship is given by the **Fisher equation**:

\[
i \approx r + \pi
\]

Where:
- $ i $ is the nominal interest rate,
- $ r $ is the real interest rate (2%),
- $ \pi $ is the expected inflation rate.

### Step 1: Calculate the Expected Inflation Rate
The inflation rate over two years can be calculated based on the changes in the Consumer Price Index (CPI). Initially, the CPI is 100, and it is expected to rise to 112.4 in two years.

The expected inflation rate over two years is:

\[
\text{Inflation rate} = \frac{112.4 - 100}{100} \times 100 = 12.4\%
\]

So, the inflation rate over two years is 12.4%.

### Step 2: Fisher Equation Application
Using the Fisher equation:

\[
i \approx 2\% + 12.4\% = 14.4\%
\]

Thus, Frank should charge a nominal interest rate of approximately **14.4%** for the loan.

### Step 3: Indexing the Loan Repayments
To ensure that Frank gets a real return of 2 percent each year, regardless of the actual inflation rate, he should adjust (or **index**) Sarah's annual repayments by the inflation rate. This would mean that the nominal amount Sarah repays should increase in line with inflation, plus an additional 2% to provide Frank with his real return.

If the inflation rate is uncertain, Frank should charge **2 percent more than the inflation rate** each year to secure his desired return.

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Would you like further details on these calculations or explanations? Here are 5 related questions to deepen your understanding:

1. How does inflation impact the purchasing power of money in a loan?
2. What is the difference between real and nominal interest rates?
3. Can the Fisher equation be used for other types of financial agreements?
4. What happens if inflation exceeds the expected rate during the loan period?
5. How does indexing a loan protect lenders from inflation risk?

**Tip:** Always separate the effects of inflation from real returns when evaluating loan agreements or investments.

Frank is lending $1,000 to Sarah for two years. Frank and Sarah agree that Frank should earn a real return of 2 percent per year. The CPI is 100 at the time that Frank makes the loan. It is expected to be 106 in one year and 112.4 in two years. What nominal rate of interest should Frank charge Sarah?

Learn how to calculate the nominal interest rate Frank should charge Sarah for a loan over two years, using the Fisher equation. This problem explains inflation rates, real and nominal interest rates, and step-by-step Fisher equation application. Suitable for students in Grades 10-12.

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