Question

ust a quick question. How am I supposed to approach this, obviously I'm given two growth rates but I'm not sure what to do with them: Suppose one year ago the price index was 120 and Amy purchased $20,000 worth of bonds. One year later the price index is 126. Amy redeems her bonds for $22,250 and is in a 40 percent tax bracket. What is Amy’s real after-tax rate of interest?

Answer 1

To find Amy's real after-tax rate of interest, calculate the nominal interest rate from her bond's increase in value, adjust for taxes, calculate the inflation rate using the price index change, and then use the formula to account for both taxes and inflation.

Step-by-step explanation:

To calculate Amy's real after-tax rate of interest, you must consider both the nominal interest she earned on her bonds and the effect of inflation and taxes on her return. The nominal interest can be calculated by the increase in value of the bonds, while the real rate of interest accounts for inflation. Finally, you must adjust for the taxes she has to pay. Here are the steps:

1. Calculate the nominal interest rate: ($22,250 - $20,000) / $20,000 = 0.1125 or 11.25%.
2. Calculate the inflation rate based on the price index increase: (126 - 120) / 120 = 0.05 or 5%.
3. Determine the after-tax nominal return: 11.25% * (1 - 0.4) = 6.75%.
4. Calculate the real after-tax rate of interest using the formula (1 + nominal after-tax interest rate) / (1 + inflation rate) - 1.

In this case: (1 + 0.0675) / (1 + 0.05) - 1 = 0.0167 or 1.67% as Amy's real after-tax rate of interest.