Questions: Dr. Fowler has 100,000, which she can put in two different types of accounts at a bank. Account A pays an interest rate of 9 percent per year; account B pays an interest rate of 3 percent per year plus the rate of inflation. Calculate the amount of money Dr. Fowler will have at the end of one year in each account if the inflation rate is 5 percent. What is the real rate of return in each case?

Dr. Fowler has 100,000, which she can put in two different types of accounts at a bank. Account A pays an interest rate of 9 percent per year; account B pays an interest rate of 3 percent per year plus the rate of inflation. Calculate the amount of money Dr. Fowler will have at the end of one year in each account if the inflation rate is 5 percent. What is the real rate of return in each case?
Transcript text: Dr. Fowler has $\$ 100,000$, which she can put in two different types of accounts at a bank. Account A pays an interest rate of 9 percent per year; account $B$ pays an interest rate of 3 percent per year plus the rate of inflation. Calculate the amount of money Dr. Fowler will have at the end of one year in each account if the inflation rate is 5 percent. What is the real rate of return in each case?
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Solution

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Solution Steps

To solve this problem, we need to calculate the amount of money in each account after one year, considering the given interest rates and inflation. For Account A, we apply the 9% interest rate directly. For Account B, we add the inflation rate to the 3% interest rate to get the total interest rate for the year. After calculating the final amounts, we determine the real rate of return by adjusting for inflation.

Step 1: Calculate the Final Amount in Account A

To find the final amount in Account A, we apply the interest rate of 9% to the initial amount of \$100,000. The formula for the final amount is:

\[ \text{Final Amount in A} = \text{Initial Amount} \times (1 + \text{Interest Rate A}) \]

Substituting the given values:

\[ \text{Final Amount in A} = 100,000 \times (1 + 0.09) = 109,000 \]

Step 2: Calculate the Final Amount in Account B

For Account B, the interest rate is 3% plus the inflation rate of 5%, totaling 8%. The formula for the final amount is:

\[ \text{Final Amount in B} = \text{Initial Amount} \times (1 + \text{Interest Rate B} + \text{Inflation Rate}) \]

Substituting the given values:

\[ \text{Final Amount in B} = 100,000 \times (1 + 0.03 + 0.05) = 108,000 \]

Step 3: Calculate the Real Rate of Return for Account A

The real rate of return adjusts the nominal return for inflation. The formula is:

\[ \text{Real Rate A} = \left(\frac{\text{Final Amount in A}}{\text{Initial Amount}} - 1\right) - \text{Inflation Rate} \]

Substituting the calculated final amount:

\[ \text{Real Rate A} = \left(\frac{109,000}{100,000} - 1\right) - 0.05 = 0.04 \]

Step 4: Calculate the Real Rate of Return for Account B

Similarly, the real rate of return for Account B is:

\[ \text{Real Rate B} = \left(\frac{\text{Final Amount in B}}{\text{Initial Amount}} - 1\right) - \text{Inflation Rate} \]

Substituting the calculated final amount:

\[ \text{Real Rate B} = \left(\frac{108,000}{100,000} - 1\right) - 0.05 = 0.03 \]

Final Answer

  • The final amount in Account A is \(\boxed{109,000}\).
  • The final amount in Account B is \(\boxed{108,000}\).
  • The real rate of return for Account A is \(\boxed{0.04}\).
  • The real rate of return for Account B is \(\boxed{0.03}\).
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