What is the approximate yield to maturity for a​ $1,000 par value bond selling for​ $1,120 that matures in 6 years and pays 12 percent interest​ annually?
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Part 1
A.
9.3 percent
B.
8.5 percent
C.
13.2 percent
D.
12.0 percent

To calculate the **Yield to Maturity (YTM)** for a bond, we use the following formula:

\[
\text{YTM} \approx \frac{C + \frac{F - P}{n}}{\frac{F + P}{2}}
\]

Where:
- $ C $ = annual coupon payment
- $ F $ = face value (or par value) of the bond
- $ P $ = current price of the bond
- $ n $ = number of years to maturity

Given:
- Par value $ F = 1000 $ dollars
- Current price $ P = 1120 $ dollars
- Coupon rate = 12%, so the annual coupon payment $ C = 0.12 \times 1000 = 120 $ dollars
- Years to maturity $ n = 6 $ years

Now, plugging the values into the formula:

\[
\text{YTM} \approx \frac{120 + \frac{1000 - 1120}{6}}{\frac{1000 + 1120}{2}}
\]

Let's calculate it step by step.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, you can calculate the approximate YTM using the formula I provided earlier. Here are the steps:

1. Compute the annual coupon payment: $ C = 120 $ dollars.
2. Subtract the bond price from the par value, then divide by years to maturity: 
\[
\frac{1000 - 1120}{6} = -20
\]
3. Add this to the coupon payment: 
\[
120 + (-20) = 100
\]
4. Calculate the average of the bond price and the par value: 
\[
\frac{1000 + 1120}{2} = 1060
\]
5. Divide step 3 by step 4: 
\[
\frac{100}{1060} \approx 0.0943 = 9.43\%
\]

Thus, the approximate yield to maturity is **9.43%**, which rounds to **9.3%** (Option A).

Would you like more details or have any questions?

Here are some related questions to explore:
1. How does the bond price affect yield to maturity?
2. What is the difference between current yield and yield to maturity?
3. How would a change in interest rates impact the bond’s YTM?
4. What is the significance of yield to maturity for bond investors?
5. How is the YTM affected if the bond is callable?

**Tip**: YTM is a key metric for comparing bonds, as it considers both coupon income and capital gain/loss over time.

What is the approximate yield to maturity for a $1,000 par value bond selling for $1,120 that matures in 6 years and pays 12 percent interest annually?

This guide explains how to calculate the approximate yield to maturity (YTM) for a $1,000 par value bond selling at $1,120, maturing in 6 years, and paying 12% interest annually. Learn step-by-step how to apply the YTM formula to find an approximate result of 9.3%.

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