Question

Question 1
Suppose that you have purchased a 3-year zero-coupon bond with face value of $1000 and a price of $850. If you hold the bond to maturity, what is your annual return?

*Make sure to input all currency answers without any currency symbols or commas, and use two decimal places of precision.

Answer 1

To calculate the annual return for a zero-coupon bond, you can use the following formula for the annual yield:

\[
\text{Annual Return} = \left( \frac{\text{Face Value}}{\text{Price}} \right)^{\frac{1}{n}} - 1
\]

Where:
- Face Value = $1000
- Price = $850
- n = 3 years

Now substituting the values into the formula:

\[
\text{Annual Return} = \left( \frac{1000}{850} \right)^{\frac{1}{3}} - 1
\]

First, calculate \(\frac{1000}{850}\):

\[
\frac{1000}{850} \approx 1.17647
\]

Next, take the cube root of this result:

\[
\left( 1.17647 \right)^{\frac{1}{3}} \approx 1.0577
\]

Now, subtract 1 from this:

\[
1.0577 - 1 \approx 0.0577
\]

Finally, convert this to a percentage:

\[
0.0577 \times 100 \approx 5.77
\]

Thus, the annual return is approximately:

\[
5.77
\]

So, the final answer is:

5.77