Question

You purchased a zero-coupon bond one year ago for $284.46. The market interest rate is now 5.1 percent. If the bond had 25 years to maturity when you originally purchased it, what was your total return for the past year? Assume semiannual compounding Note: Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, 32.16.

Answer 1

your total return for the past year, expressed as a percent rounded to two decimal places, is 4.97%.

To calculate the total return for the past year on the zero-coupon bond, we need to follow these steps:

1. Calculate the bond's value at the beginning of the year (which we have as $284.46).

2. Determine the bond's value at the end of the year using the new market interest rate (5.1% with semiannual compounding).

3. Calculate the total return, which is the change in value over the initial value, as a percentage.

Given that the bond had 25 years to maturity when purchased, it now has 24 years to maturity. The price of a zero-coupon bond can be calculated using the formula:

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

Where:

-
`\( P \)` is the price of the bond

-
`\( M \)` is the maturity value (face value, which we'll assume is $1,000 unless given otherwise)

-
`\( r \)` is the annual market interest rate (5.1% or 0.051)

-
`\( n \)` is the number of compounding periods per year (2 for semiannual)

-
`\( t \)` is the number of years until maturity (24 years now)

The bond's value at the end of one year is calculated based on the remaining 24 years using the new market interest rate. We need to solve for
`\( P \)` using the given
`\( r \)`,
`\( n \)`, and
`\( t \)`.

Let's do the calculations.

The bond's value at the end of the year, using the current market interest rate, is approximately $298.60. The total return for the past year on the zero-coupon bond is approximately 4.97%.

Therefore, your total return for the past year, expressed as a percent rounded to two decimal places, is 4.97%.