To solve this, we first need to determine the price of the zero-coupon bond, calculate the income earned, and then apply the tax rate to find the after-tax cash flow.

Step 1: Calculate the price of the bond

Since this is a zero-coupon bond, it pays no interest. The price is determined by discounting the face value using the yield to maturity (YTM). Given that the YTM is compounded semi-annually, the formula for the bond price $P$ is:

$P = \frac{F}{(1 + \frac{YTM}{2})^{2}}$

Where:

• $F$ is the face value = 1000
• $YTM$ is the yield to maturity = 10.4% or 0.104
• The exponent 2 represents the two periods in one year (semi-annual).

Plugging in the values:

= \frac{1000}{(1 + 0.052)^2} = \frac{1000}{(1.052)^2} = \frac{1000}{1.106704}$$ $$P \approx 903.47$$ So, the bond price is approximately 903.47. ### Step 2: Calculate the income earned The income earned on the bond over one year is the difference between the face value and the price of the bond: $$Income = 1000 - 903.47 = 96.53$$ ### Step 3: Apply the tax rate Since the personal income tax rate is 29%, the tax on the income is: $$Tax = 0.29 \times 96.53 = 27.99$$ ### Step 4: Calculate the after-tax cash flow The after-tax cash flow is the face value minus the tax: $$\text{After-tax cash flow} = 1000 - 27.99 = 972.01$$ Thus, your after-tax cash flow one year from now is **972.01**. --- Would you like further details on any of the steps? Here are some related questions to explore this topic further: 1. What happens to the bond price if the YTM increases? 2. How would the after-tax cash flow change if the tax rate was 35% instead of 29%? 3. How does the semi-annual compounding impact the bond price calculation? 4. What is the relationship between YTM and bond price for zero-coupon bonds? 5. How can one calculate the total return on a bond investment? **Tip**: Zero-coupon bonds offer no periodic interest payments, but they allow for significant capital gains, which are subject to tax. Always factor in your tax rate when calculating investment returns.