What is the inflation rate when the real interest rate is 2.5% and the nominal interest rate is 8.4%?
The correct answer and explanation is:
To calculate the inflation rate, we can use the Fisher Equation, which is a formula that relates nominal interest rates, real interest rates, and inflation rates. The equation is: (1+i)=(1+r)(1+π)(1 + i) = (1 + r)(1 + \pi)
Where:
- ii is the nominal interest rate
- rr is the real interest rate
- π\pi is the inflation rate
In this case, we know that:
- The real interest rate r=2.5%r = 2.5\% or 0.025
- The nominal interest rate i=8.4%i = 8.4\% or 0.084
We can solve for π\pi (the inflation rate) by rearranging the Fisher Equation: (1+i)=(1+r)(1+π)(1 + i) = (1 + r)(1 + \pi)
Substituting the given values: (1+0.084)=(1+0.025)(1+π)(1 + 0.084) = (1 + 0.025)(1 + \pi) 1.084=1.025(1+π)1.084 = 1.025(1 + \pi)
Now, divide both sides by 1.025 to isolate (1+π)(1 + \pi): 1.0841.025=1+π\frac{1.084}{1.025} = 1 + \pi 1.059=1+π1.059 = 1 + \pi
Now, subtract 1 from both sides: π=1.059−1=0.059\pi = 1.059 – 1 = 0.059
Therefore, the inflation rate π=0.059\pi = 0.059 or 5.9%.
Explanation:
The Fisher Equation shows the relationship between the nominal interest rate, the real interest rate, and the inflation rate. The nominal interest rate is the rate at which money grows, while the real interest rate is the rate adjusted for inflation, representing the actual purchasing power increase. By using the Fisher Equation, we can compute the inflation rate by knowing the real and nominal rates. In this case, the inflation rate is 5.9%, meaning prices are increasing at that rate annually. The Fisher Equation assumes that inflation and interest rates are relatively stable, and the relationship is logarithmic rather than simple addition.