At what price should a bond with a coupon rate of 5% and 12 years to maturity sell for if bonds of similar risk are currently selling to yield a 3.25% return

To calculate the price of the bond, we will use the **Present Value (PV) of future cash flows** method. A bond's price is the sum of the present value of its coupon payments and the present value of its face value (also called par value) at maturity.

Here’s the step-by-step approach:

1. **Coupon Payment**: 
   The bond has a coupon rate of 5%, which means it pays 5% of its face value as interest annually. Let’s assume the face value (par value) of the bond is \$1,000 (this is standard unless stated otherwise).
   
   Coupon Payment = $ 5\% \times 1,000 = 50 $ per year.

2. **Yield to Maturity (YTM)**: 
   The market is yielding 3.25%, meaning that the present value of the bond's cash flows should be discounted using 3.25% as the interest rate.

3. **Time to Maturity**: 
   The bond matures in 12 years, meaning you’ll receive 12 coupon payments plus the repayment of the face value at the end.

### Formula for Bond Price
The bond price is calculated as:

\[
P = C \times \left(1 - \frac{1}{(1 + r)^t}\right) \div r + \frac{F}{(1 + r)^t}
\]

Where:
- $ P $ = price of the bond
- $ C $ = coupon payment per period (\$50 annually)
- $ r $ = yield per period (3.25% or 0.0325)
- $ t $ = number of periods (12 years)
- $ F $ = face value (\$1,000)

Let’s now calculate this.

The bond should sell for approximately **$1,171.62**.

This price is higher than the bond's face value (\$1,000) because the bond's coupon rate (5%) is higher than the current market yield (3.25%), making it more attractive.

Would you like further details or have any other questions?

Here are 5 related questions to explore:

1. How does the bond price change if the yield increases to 4%?
2. What happens to the bond price if the maturity is shortened to 10 years?
3. How is the price of a zero-coupon bond calculated?
4. What is the relationship between bond prices and interest rates?
5. How do callable bonds differ in pricing compared to regular bonds?

**Tip**: When the market interest rate (yield) is lower than a bond's coupon rate, the bond typically trades at a premium (above face value).

At what price should a bond with a coupon rate of 5% and 12 years to maturity sell for if bonds of similar risk are currently selling to yield a 3.25% return?

Learn how to calculate the price of a bond with a 5% coupon rate and 12 years to maturity when similar bonds are yielding 3.25%. This detailed guide covers the present value of coupon payments and the face value at maturity, with a step-by-step formula-based solution. Suitable for advanced high school and undergraduate finance students.

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