A zero coupon bond with face value of $1,000 and 5.00 years to maturity sells for $858.00. What is the discount rate for the bond?

Answer 1

To calculate the discount rate for a zero coupon bond, we can use the present value formula for a single future cash flow:

\[ PV = \frac{FV}{(1 + r)^n} \]

Where:

• \( PV \) = Present Value (current selling price of the bond, $858.00)
• \( FV \) = Future Value (face value of the bond, $1,000)
• \( r \) = discount rate (annual)
• \( n \) = number of years to maturity (5.00 years)

Rearranging the formula to solve for \( r \) gives:

\[ r = \left(\frac{FV}{PV}\right)^{\frac{1}{n}} - 1 \]

Plugging in the values:

\[ r = \left(\frac{1000}{858}\right)^{\frac{1}{5}} - 1 \]

Calculating it step by step:

1. Divide \( 1000 \) by \( 858 \):

\[ \frac{1000}{858} \approx 1.1655 \]

2. Raise this result to the power of \( \frac{1}{5} \):

\[ (1.1655)^{\frac{1}{5}} \approx 1.0315 \]

3. Subtract 1:

\[ 1.0315 - 1 \approx 0.0315 \]

4. Convert to percentage:

\[ r \approx 0.0315 \times 100 \approx 3.15% \]

So, the discount rate for the bond is approximately 3.15%.