Frank is going to lend Sarah $1000 for 1 year. Frank and Sarah agree that Frank should earn a 2% real rate of interest on the loan. The CPI index is 100 at the time Frank makes the loan and is expected to be 110 in one year. What nominal rate of interest should Frank charge Sarah?Group of answer choices14%12%10%8%
Question
Frank is going to lend Sarah $1000 for 1 year. Frank and Sarah agree that Frank should earn a 2% real rate of interest on the loan. The CPI index is 100 at the time Frank makes the loan and is expected to be 110 in one year. What nominal rate of interest should Frank charge Sarah?Group of answer choices14%12%10%8%
Solution
The nominal interest rate can be calculated using the Fisher equation, which states that the nominal interest rate is approximately the sum of the real interest rate and the expected inflation rate.
Step 1: Identify the real interest rate. From the problem, we know that the real interest rate is 2%.
Step 2: Calculate the expected inflation rate. The expected inflation rate can be calculated by taking the expected CPI index in one year, subtracting the current CPI index, and then dividing by the current CPI index.
Expected inflation rate = (Expected CPI - Current CPI) / Current CPI Expected inflation rate = (110 - 100) / 100 = 10%
Step 3: Calculate the nominal interest rate. According to the Fisher equation, the nominal interest rate is the sum of the real interest rate and the expected inflation rate.
Nominal interest rate = Real interest rate + Expected inflation rate Nominal interest rate = 2% + 10% = 12%
So, Frank should charge Sarah a nominal interest rate of 12%.
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