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 on a zero-coupon bond, you can use the following formula for the annualized return:

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

where \( n \) is the number of years to maturity.

In this case:

- Face Value = $1000
- Purchase Price = $850
- n = 3 years

Now, we can plug in the values:

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

Calculating the ratio:

\[
\frac{1000}{850} \approx 1.1765
\]

Now, calculating the cube root:

\[
1.1765^{\frac{1}{3}} \approx 1.05787
\]

So, the annual return calculation is:

\[
\text{Annual Return} \approx 1.05787 - 1 \approx 0.05787
\]

Now, convert to percentage:

\[
\text{Annual Return} \approx 0.05787 \times 100 \approx 5.79\%
\]

Thus, the annual return is approximately:

\[
\text{Annual Return} = 5.79
\]

Final answer: **5.79**