QuestionJuly 12, 2025

Show Calculation: If the nominal interest rate is 7 percent and the real interest rate is 3 percent, then the inflation rate is __ percent. __

Show Calculation: If the nominal interest rate is 7 percent and the real interest rate is 3 percent, then the inflation rate is __ percent. __
Show Calculation: If the nominal interest rate is 7 percent and the real interest rate is 3 percent, then the inflation rate is __ percent. __

Solution
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Answer

3.88 percent Explanation 1. Identify the formula Use the Fisher equation: **1 + i = (1 + r)(1 + \pi)**, where i is the nominal interest rate, r is the real interest rate, and \pi is the inflation rate. 2. Substitute known values Given i = 0.07 and r = 0.03, substitute into the formula: 1 + 0.07 = (1 + 0.03)(1 + \pi). 3. Solve for inflation rate Simplify to find \pi: 1.07 = 1.03(1 + \pi). Divide both sides by 1.03: 1 + \pi = \frac{1.07}{1.03}. Calculate \pi: \pi = \frac{1.07}{1.03} - 1. 4. Calculate the result Compute \pi: \pi = 0.0388 or approximately 3.88%.

Explanation

1. Identify the formula<br /> Use the Fisher equation: **$1 + i = (1 + r)(1 + \pi)$**, where $i$ is the nominal interest rate, $r$ is the real interest rate, and $\pi$ is the inflation rate.<br /><br />2. Substitute known values<br /> Given $i = 0.07$ and $r = 0.03$, substitute into the formula: $1 + 0.07 = (1 + 0.03)(1 + \pi)$.<br /><br />3. Solve for inflation rate<br /> Simplify to find $\pi$: $1.07 = 1.03(1 + \pi)$. Divide both sides by 1.03: $1 + \pi = \frac{1.07}{1.03}$. Calculate $\pi$: $\pi = \frac{1.07}{1.03} - 1$.<br /><br />4. Calculate the result<br /> Compute $\pi$: $\pi = 0.0388$ or approximately 3.88%.
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