Susan purchases a bond that has a maturity of 4 years. The bond pays
an annual coupon rate of 5% but makes semiannual coupon payments. The par
value is $1000 and the bond’s yield to maturity is 8.6%. What is the bond’s
current price?

To calculate the bond’s current price, we will use the **present value formula** for bonds. The price of a bond is the sum of the present value of its coupon payments and the present value of its face value at maturity.

Given:
- **Coupon rate** = 5% annually
- **Par value** = $1,000
- **Semiannual coupon payments**: 5% annual coupon rate means 2.5% per semiannual period
- **Years to maturity** = 4 years
- **Semiannual periods** = 4 years × 2 = 8 periods
- **Yield to maturity (YTM)** = 8.6% annually, so 4.3% per semiannual period

We calculate the bond price in two parts:
1. **Present value of coupon payments**: The bond makes semiannual coupon payments of $ 2.5\% \times 1000 = 25 $ dollars for 8 periods.
2. **Present value of the face value**: The face value of $1,000 is paid at the end of 8 periods.

### Formula:
\[
\text{Price of bond} = C \times \left(1 - \left(1 + r\right)^{-n}\right) \div r + \frac{F}{\left(1 + r\right)^n}
\]
Where:
- $ C $ = Coupon payment per period = 25
- $ r $ = Yield per period = 4.3% = 0.043
- $ n $ = Number of periods = 8
- $ F $ = Face value = 1,000

Let me calculate the current bond price.The current price of the bond is approximately **$880.30**.

Would you like any further details or explanations?

Here are 5 related questions you might consider:
1. How does the bond price change if the yield to maturity decreases?
2. What is the relationship between bond prices and interest rates?
3. How would the bond price change if it made annual coupon payments instead of semiannual?
4. What would happen to the bond price if the time to maturity increased?
5. How do we calculate the bond’s current yield?

**Tip:** When bond yields rise, the bond price falls, and vice versa—this inverse relationship is key to understanding bond market dynamics.

Susan purchases a bond that has a maturity of 4 years. The bond pays an annual coupon rate of 5% but makes semiannual coupon payments. The par value is $1000 and the bond’s yield to maturity is 8.6%. What is the bond’s current price?

Learn how to calculate the current price of a bond with semiannual coupon payments, a 5% annual coupon rate, 4 years to maturity, and a yield to maturity of 8.6%. This detailed example demonstrates key financial concepts such as present value and bond pricing. Suitable for finance and economics students.

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