Answer :
Final Answer:
The interest rate is approximately 1.09%.
Explanation:
To find the interest rate, we can use the formula for calculating the real interest rate. The real interest rate takes into account the change in the Consumer Price Index (CPI), which measures inflation.
The formula for the real interest rate is:
[tex]\[Real\ Interest\ Rate = \frac{Nominal\ Interest\ Rate - Inflation\ Rate}{1 + Inflation\ Rate}\][/tex]
Given that the nominal interest rate is 8%, we need to find the inflation rate. The change in the CPI can be used to calculate the inflation rate as follows:
[tex]\[Inflation\ Rate = \frac{CPI_{new} - CPI_{old}}{CPI_{old}}\][/tex]
Substituting the values:
[tex]\[Inflation\ Rate = \frac{102.3 - 101.2}{101.2} \approx 0.0109\][/tex]
Now, we can use the real interest rate formula:
[tex]\[Real\ Interest\ Rate = \frac{0.08 - 0.0109}{1 + 0.0109} \approx \frac{0.0691}{1.0109} \approx 0.0683\][/tex]
To express the interest rate as a percentage, multiply by 100:
Real Interest Rate ≈ 6.83%
So, the interest rate is approximately 6.83%.
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