You are called in as a financial analyst to appraise the bonds of Olsen’s Clothing Stores. The $1,000 par value bonds have a quoted annual interest rate of 12 percent, which is paid semiannually. The yield to maturity on the bonds is 12 percent annual interest. There are 10 years to maturity. Compute the price of the bonds based on semiannual analysis

To compute the price of Olsen's Clothing Stores' bonds, we will use the present value formula for bonds. The bond price is the sum of the present value of the coupon payments and the present value of the face value (par value) of the bond, discounted at the bond's yield to maturity (YTM).

### Given Information:
- **Par value** $ (FV) = 1000 $ 
- **Coupon rate** = 12% annually (paid semiannually, so each period's rate is 6%)
- **Semiannual coupon payment** = $ \frac{12\%}{2} \times 1000 = 60 $ 
- **Yield to maturity (YTM)** = 12% annually (so 6% per semiannual period)
- **Number of years to maturity** = 10 years (semiannual periods $ = 10 \times 2 = 20 $ periods)

### Formula:
The price $ P $ of the bond can be found using the formula:

\[
P = C \times \left( 1 - (1 + r)^{-n} \right) / r + \frac{FV}{(1 + r)^n}
\]

Where:
- $ C $ = Semiannual coupon payment = $60
- $ r $ = Semiannual yield to maturity = 6% = 0.06
- $ n $ = Total number of semiannual periods = 20
- $ FV $ = Face value (par value) = $1,000

Let's compute this using the formula.The price of Olsen's Clothing Stores' bond is \$1,000. Since the yield to maturity matches the coupon rate, the bond is priced at par value.

Would you like more details or have any questions?

Here are some related questions to explore further:
1. What happens to the bond price if the yield to maturity increases?
2. How does a bond's price change if interest is compounded quarterly instead of semiannually?
3. What is the relationship between bond prices and interest rates?
4. Can you explain the difference between premium, par, and discount bonds?
5. How would the price change if the coupon rate was lower than the yield to maturity?

**Tip:** A bond priced at par occurs when the coupon rate equals the yield to maturity.

You are called in as a financial analyst to appraise the bonds of Olsen’s Clothing Stores. The $1,000 par value bonds have a quoted annual interest rate of 12 percent, which is paid semiannually. The yield to maturity on the bonds is 12 percent annual interest. There are 10 years to maturity. Compute the price of the bonds based on semiannual analysis.

Learn how to calculate the price of a $1,000 par value bond for Olsen’s Clothing Stores, with a 12% annual coupon rate and yield to maturity, using semiannual analysis. Understand the present value of coupon payments and face value over a 10-year period.

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