A firm has some bonds maturing in 12 years, with par value of $1,000. Those bonds make annual coupon payment of $70.  The market interest rate on similar bonds is 8.5%.  What is the bond's price?
Group of answer choices

$815.45

$889.83

$1,085.36

$1,102.84

$923.22

To determine the price of the bond, we can use the **present value formula** for bonds, which accounts for both the **present value of the coupon payments** (annuity) and the **present value of the par value** (lump sum at maturity). The bond price is the sum of these two present values:

1. **Coupon payments (Annuity):**
   The bond pays an annual coupon of $70 for 12 years. The present value of these coupon payments is calculated using the formula for the present value of an annuity:

   \[
   PV_{\text{coupons}} = C \times \left(1 - \left(1 + r\right)^{-t}\right) \div r
   \]

   Where:
   - $ C = 70 $ (annual coupon payment)
   - $ r = 0.085 $ (market interest rate as a decimal)
   - $ t = 12 $ (number of years)

2. **Par value (Lump sum):**
   The bond's par value of $1,000 will be paid at maturity in 12 years. The present value of this lump sum is calculated using the formula:

   \[
   PV_{\text{par}} = \frac{F}{(1 + r)^t}
   \]

   Where:
   - $ F = 1,000 $ (face value)
   - $ r = 0.085 $
   - $ t = 12 $

Let's calculate this step by step.

### Step 1: Calculate the present value of the coupon payments

\[
PV_{\text{coupons}} = 70 \times \left(1 - \left(1 + 0.085\right)^{-12}\right) \div 0.085
\]

### Step 2: Calculate the present value of the par value

\[
PV_{\text{par}} = \frac{1,000}{(1 + 0.085)^{12}}
\]

Finally, adding both present values will give the bond's price. I'll compute this now.The price of the bond is approximately **$889.83**. Therefore, the correct answer is:

**$889.83**

Would you like more details or have any questions?

Here are some related questions:
1. How does the bond price change if the market interest rate increases?
2. What would be the bond price if the coupon payments were semi-annual instead of annual?
3. How is the bond's duration related to its price sensitivity to interest rates?
4. What is the impact of time to maturity on the bond price?
5. How do zero-coupon bonds differ in pricing from coupon bonds?

**Tip:** When market interest rates rise, bond prices fall, and vice versa. This inverse relationship is fundamental to bond pricing.

A firm has some bonds maturing in 12 years, with par value of $1,000. Those bonds make annual coupon payment of $70. The market interest rate on similar bonds is 8.5%. What is the bond's price?

Calculate the price of a bond with a 12-year maturity, $1,000 par value, $70 annual coupon payment, and 8.5% market interest rate. Learn how present value and annuity formulas apply to bond pricing.

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