Suppose that a zero-coupon bond with a face value of 10542 and time to maturity of 5 years is trading at $ 8471 . What is its yield to maturity (YTM)?

To find the yield to maturity (YTM) for a zero-coupon bond, we use the formula:

\[
P = \frac{F}{(1 + YTM)^T}
\]

Where:
- $ P $ is the present price of the bond (8471).
- $ F $ is the face value of the bond (10542).
- $ T $ is the time to maturity (5 years).
- $ YTM $ is the yield to maturity (the unknown we need to calculate).

Rearranging the formula to solve for YTM:

\[
YTM = \left( \frac{F}{P} \right)^{\frac{1}{T}} - 1
\]

Now, let's compute the YTM.

\[
YTM = \left( \frac{10542}{8471} \right)^{\frac{1}{5}} - 1
\]

I'll calculate this for you.The yield to maturity (YTM) for the zero-coupon bond is approximately **4.47%**.

Would you like further details or have any questions about this calculation?

Here are 5 related questions to deepen your understanding:
1. How does the YTM of a zero-coupon bond differ from that of a coupon-paying bond?
2. How does an increase in the bond price affect the YTM?
3. What are the risks associated with investing in zero-coupon bonds?
4. How would inflation impact the real return on a zero-coupon bond?
5. How can you estimate the YTM for bonds with multiple cash flows?

**Tip**: As the bond price decreases, the yield to maturity increases, as you're paying less today for the same future value!

Learn how to calculate the yield to maturity (YTM) for a zero-coupon bond with a face value of 10542, trading at a price of 8471, and maturing in 5 years. This problem uses the time value of money principles and bond pricing formulas to find the YTM, suitable for advanced high school math or undergraduate finance students.

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