Question

Question 3
Suppose you bought a five-year zero-coupon Treasury bond for $800 per $1000 face value. What is the yield to maturity (annual compounding) on the bond?

*Make sure to input all percentage answers as numeric values without symbols, and use four decimal places of precision. For example, if the answer is 6%, then enter 0.0600.

Answer 1

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

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

Where:
- \( F \) is the face value of the bond,
- \( P \) is the purchase price of the bond,
- \( n \) is the number of years until maturity.

In your case:
- \( F = 1000 \) (the face value),
- \( P = 800 \) (the purchase price),
- \( n = 5 \) (the number of years).

Now plug these values into the formula:

\[
YTM = \left( \frac{1000}{800} \right)^{\frac{1}{5}} - 1
\]

Calculating \( \frac{1000}{800} \):

\[
\frac{1000}{800} = 1.25
\]

Now substituting that back into the YTM formula:

\[
YTM = (1.25)^{\frac{1}{5}} - 1
\]

Now calculate \( (1.25)^{\frac{1}{5}} \):

Using a calculator, we find:

\[
(1.25)^{\frac{1}{5}} \approx 1.04712854805
\]

Now subtract 1:

\[
YTM \approx 1.04712854805 - 1 \approx 0.04712854805
\]

Now convert this to a percentage format:

\[
YTM \approx 0.0471 \text{ or } 4.712854805\%
\]

Now round it to four decimal places for the final answer:

\[
YTM \approx 0.0471
\]

So, the yield to maturity on the bond is:

\[
\boxed{0.0471}
\]