Question
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A bond that pays interest annually yields a rate of return of 5.75 percent. The inflation rate for the same period is 3 percent. What is the real rate of return on this bond?

Ask by Mccarthy Maxwell. in the United States
Feb 26,2025

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Answer

The real rate of return on the bond is approximately 2.77%.

Solution

To calculate the real rate of return, we use the Fisher equation, which relates the nominal rate (i), the inflation rate (π), and the real rate (r) as follows:   (1 + i) = (1 + r) × (1 + π) Given:   Nominal rate, i = 5.75% = 0.0575   Inflation rate, π = 3% = 0.03 Step 1: Rearrange the formula to solve for r:   1 + r = (1 + i) / (1 + π) Step 2: Substitute the given values:   1 + r = (1 + 0.0575) / (1 + 0.03)   1 + r = 1.0575 / 1.03 Step 3: Perform the division:   1 + r ≈ 1.02767 Step 4: Solve for r:   r ≈ 1.02767 - 1   r ≈ 0.02767 or 2.77% So, the real rate of return on the bond is approximately 2.77%.

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To find the real rate of return on the bond, you can use the Fisher equation: \( (1 + nominal rate) = (1 + real rate) \times (1 + inflation rate) \). Plugging in the numbers, rearranging, and calculating gives you a real rate of return of approximately 2.69 percent. This means that after accounting for inflation, your purchasing power is still growing, just at a slower pace than the nominal return might suggest! When investing in bonds or any fixed-income assets, it’s essential to consider interest rates and inflation together. A common mistake is to focus solely on the nominal yield without factoring in how inflation can erode earnings. Always calculate the real return to understand the true increase in your wealth!

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