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Joaquin wants to earn a real annual interest rate on his investment of at least 12%. If the annual rate of inflation is 4%, what is the minimum nominal rate of interest Joao would be willing to accept on his investment?

Question

Joaquin wants to earn a real annual interest rate on his investment of at least 12%. If the annual rate of inflation is 4%, what is the minimum nominal rate of interest Joao would be willing to accept on his investment?

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Solution

To calculate the minimum nominal rate of interest Joaquin would be willing to accept on his investment, we need to use the Fisher equation, which is used to relate the real interest rate, the nominal interest rate, and the inflation rate. The Fisher equation is:

1 + nominal rate = (1 + real rate) * (1 + inflation rate)

Joaquin wants to earn a real annual interest rate of at least 12% or 0.12 in decimal form, and the annual rate of inflation is 4% or 0.04 in decimal form. Substituting these values into the Fisher equation gives:

1 + nominal rate = (1 + 0.12) * (1 + 0.04)

Solving this equation for the nominal rate gives:

nominal rate = (1 + 0.12) * (1 + 0.04) - 1

nominal rate = 1.12 * 1.04 - 1

nominal rate = 1.1648 - 1

nominal rate = 0.1648

So, the minimum nominal rate of interest Joaquin would be willing to accept on his investment is 16.48%.

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