Final answer:
Residents of New South Brazillia need a nominal interest rate of approximately 40.8% or an exact rate of 41.502% to stay ahead of inflation and maintain a real interest rate of 1.8%, using the approximate and exact Fisher equations respectively.
Step-by-step explanation:
The student is asking about how to calculate the nominal interest rate that residents of New South Brazillia must receive to stay ahead of inflation and still earn a real rate of interest. The given annual inflation rate is 39%, and the real interest rate is 1.8%. To determine the nominal interest rate required, we use two formulas: the approximate and the exact Fisher equation. The approximate nominal interest rate is obtained by simply adding the inflation rate to the real interest rate. The exact nominal interest rate is calculated using the Fisher equation which accounts for the compounding effect of inflation.
To calculate the approximate nominal interest rate:
Nominal Interest Rate (approx) = Real Interest Rate + Inflation Rate
Nominal Interest Rate (approx) = 1.8% + 39% = 40.8%
To calculate the exact nominal interest rate using the Fisher equation:
Nominal Interest Rate (exact) = (1 + Real Interest Rate) * (1 + Inflation Rate) - 1
Nominal Interest Rate (exact) = (1 + 0.018) * (1 + 0.39) - 1
Nominal Interest Rate (exact) = (1.018 * 1.39) - 1
Nominal Interest Rate (exact) = 1.41502 - 1 = 0.41502 or 41.502%
Therefore, residents need to receive a nominal interest rate of around 40.8% or 41.502% to stay ahead of inflation and maintain the real interest rate of 1.8%.