Question

If nominal interest rate equals 5 percent and expected inflation is 3 percent, then the new nominal and real interest rates are respectively: A) 3% and 5%. B) 8% and 5%. C) 5% and 2%. D) 5% and 7%. E) 7% and 5%.

Answer 1

Answer:

C. Real Interest Rate = 2% and Nominal Rate = 5%

Explanation:

Given

Nominal Interest Rate = 5%

Expected Inflation Rate = 3%

Required

The new nominal rate

The real interest rate

First; We'll need to calculate the real interest rate

$Real\ Interest\ Rate = Nominal\ Interest\ Rate - Inflation\ Rate$

$Real\ Interest\ Rate = 5\% - 3\%$

$Real\ Interest\ Rate = 2\%$

New Nominal Rate is calculated as thus;

$Nominal\ Rate = [(1 + Real\ Interest\ Rate) * (1 + Inflation\ Rate)] - 1$

$Nominal\ Rate = [(1 + 2\%) * (1 + 3\%)] - 1$

$Nominal\ Rate = [(1 + 0.02) * (1 + 0.03)] - 1$

$Nominal\ Rate = [(1.02) * (1.03)] - 1$

$Nominal\ Rate = [(1.02 * 1.03)] - 1$

$Nominal\ Rate = 1.0506 - 1$

$Nominal\ Rate = 0.0506$

Convert to Percentage

$Nominal\ Rate = 5.06\%$

$Nominal\ Rate = 5\%$ (Approximated)