Calculate the price of a 5.3% coupon bond with a 15 year left to maturity and a market interest rate at 4.8% assume interest payments are semi annually. Is this a discount or premium bond?

To calculate the price of a bond, we can use the formula for the present value of its cash flows, which include both the coupon payments and the face value. The bond price is calculated as the sum of the present values of these future payments.

### Bond Price Formula:
\[
P = C \times \left(1 - (1 + r)^{-n}\right) \div r + \frac{F}{(1 + r)^n}
\]

Where:
- $P$ = price of the bond
- $C$ = coupon payment per period
- $F$ = face value (assume \$1000 if not given)
- $r$ = market interest rate per period
- $n$ = total number of periods

### Step-by-Step Calculation:

1. **Coupon Payment ($C$)**:  
   Since the bond has a 5.3% coupon rate and makes semi-annual payments:
   \[
   C = \frac{5.3\% \times 1000}{2} = \frac{53}{2} = 26.5
   \]

2. **Market Interest Rate per Period ($r$)**:  
   The market interest rate is 4.8% annually, so for semi-annual periods:
   \[
   r = \frac{4.8\%}{2} = 2.4\% = 0.024
   \]

3. **Number of Periods ($n$)**:  
   The bond has 15 years to maturity, with semi-annual payments:
   \[
   n = 15 \times 2 = 30
   \]

4. **Face Value ($F$)**:  
   The face value of the bond is \$1000.

### Plugging values into the formula:

\[
P = 26.5 \times \left(1 - (1 + 0.024)^{-30}\right) \div 0.024 + \frac{1000}{(1 + 0.024)^{30}}
\]

Let's calculate this.The calculated price of the bond is approximately **$1053.03**.

Since the bond's price is above its face value (\$1000), it is a **premium bond**. This happens when the coupon rate (5.3%) is higher than the market interest rate (4.8%).

### Would you like more details or have any questions?

Here are five related questions to explore:

1. How would the bond price change if the market interest rate increased?
2. What happens to bond prices as the time to maturity decreases?
3. How is the yield to maturity (YTM) calculated for this bond?
4. What is the relationship between coupon rates and bond pricing?
5. How does reinvestment risk affect bond investors?

**Tip**: When interest rates rise, bond prices fall, and vice versa. This is known as the inverse relationship between bond prices and interest rates.

Learn how to calculate the price of a 5.3% coupon bond with 15 years left to maturity and a market interest rate of 4.8%. This step-by-step solution covers key financial concepts such as bond pricing, present value of future cash flows, and how interest rate changes affect bond pricing. The calculated bond price is $1053.03, and it's determined to be a premium bond since its price is above its face value.

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