Question

Compute Bond Price (LG7-4) Compute the price of a 4.6 percent coupon bond with 10 years left to maturity and a market interest rate of 70 percent. (Assume interest payments are semiannual) Note: Do not round intermediate calculations. Round your final answer to 2 decimal places. Is this a discount or premium bond?

Answer 1

The price of the 4.6 percent coupon bond with 10 years left to maturity and a market interest rate of 7.0 percent, assuming semiannual interest payments, is $88.49. This indicates that the bond is selling at a discount.

Step-by-step explanation:

The bond price is calculated using the present value formula for a bond:

`P= rC×(1−(1+r) −nt )​ + (1+r) nt F​`

where P is the price of the bond,C is the semiannual coupon payment,r is the semiannual interest rate,n is the total number of periods (years * 2 for semiannual payments), and F is the face value of the bond.

In this case, the coupon rate is 4.6 percent, so C=4.6%/2=0.023 the market interest rate is 7.0 percent, so r =7%/2=0.035 and there are 10 years left to maturity, so n=10×2=20.The face value F is typically $1,000.

Substituting these values into the formula:

`P= 0.0350.023×(1−(1+0.035) −20 )​ + (1+0.035) 20 1000​`

After calculating this expression, we find that the bond price is $88.49.

Since the computed price is less than the face value, this bond is selling at a discount. This is because the market interest rate of 7.0 percent is higher than the bond's coupon rate of 4.6 percent, making the bond less attractive to investors, and consequently, its price is discounted.