Question

You purchased a zero-coupon bond one year ago for $282.33. The market interest rate is now 7 percent. Assume semiannual compounding. If the bond had 19 years to maturity when you originally purchased it, what was your total return for the past year? Note: Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.

Answer 1

Therefore, your total return for the past year on the zero-coupon bond is 7.12%.

To calculate the total return for the past year, we need to:

1. Calculate the value of the bond a year ago when it was purchased.

2. Calculate the value of the bond now, one year later.

3. Find the difference between the two values, which represents the gain or loss.

4. Divide the gain or loss by the original value to find the return.

5. Convert that return to a percentage and round to two decimal places.

We already have the purchase price of the bond one year ago, which is $282.33.

To find the value of the bond now, we use the formula for the future value of a zero-coupon bond, which is:

`\[ P = (M)/((1 + r/n)^(nt)) \]`

where:

-
`\( P \)` is the present value of the bond (what you would pay for it today),

-
`\( M \)` is the maturity value (face value) of the bond,

-
`\( r \)` is the annual market interest rate (as a decimal),

-
`\( n \)` is the number of compounding periods per year,

-
`\( t \)` is the number of years until maturity.

Since we don't know the face value
`\( M \)` of the bond, we'll have to rearrange the formula to solve for
`\( M \)`, using the information from one year ago when the bond had 19 years to maturity:

`\[ M = P * (1 + r/n)^(nt) \]`

Then, we can calculate the new present value of the bond,
`\( P \)`, now that the bond has 18 years to maturity. Let's perform these calculations step by step.

The face value (maturity value) of the bond calculated based on the original purchase price and the terms given is approximately $1,043.49.

The present value of the bond now, after one year with 18 years remaining to maturity, is approximately $302.44.

The total return for the past year, expressed as a percentage and rounded to two decimal places, is approximately 7.12%.

Therefore, your total return for the past year on the zero-coupon bond is 7.12%.