Question

The market price of a 15.00-year STRIPS is $371.00 The yield to maturity is ____%.

Answer 1

To calculate the yield to maturity (YTM) of a STRIPS (Separate Trading of Registered Interest and Principal of Securities), we can use the following formula for YTM with zero-coupon bonds:

\[
YTM = \left( \frac{F}{P} \right)^{\frac{1}{n}} - 1
\]

where:
- \( F \) = face value of the bond (which is typically $1,000 unless specified otherwise),
- \( P \) = current market price of the bond,
- \( n \) = number of years to maturity.

Given the values:
- \( F = 1000 \) (assuming standard face value),
- \( P = 371.00 \),
- \( n = 15.00 \).

Substituting the values into the formula gives:

\[
YTM = \left( \frac{1000}{371} \right)^{\frac{1}{15}} - 1
\]

Now, calculate \( \frac{1000}{371} \):

\[
\frac{1000}{371} \approx 2.694
\]

Next, take the 15th root of 2.694:

\[
YTM \approx \left( 2.694 \right)^{\frac{1}{15}} - 1
\]

Calculating the 15th root of 2.694 (which can be done using a scientific calculator or software):

\[
YTM \approx 1.0756 - 1
\]

Finally:

\[
YTM \approx 0.0756
\]

Multiplying by 100 to express this as a percentage:

\[
YTM \approx 7.56\%
\]

Thus, the yield to maturity (YTM) of the 15.00-year STRIPS is approximately **7.56%**.