Final answer:
To compute the price of a bond with 10 years left to maturity and a market interest rate of 10.2 percent, we can use the formula for the present value of a bond. The price of the bond is $855.50.
Step-by-step explanation:
To compute the price of a bond with 10 years left to maturity and a market interest rate of 10.2 percent, we can use the formula for the present value of a bond. The present value is the sum of the present values of all future cash flows of the bond, discounted at the market interest rate. In this case, the bond has a 6.2 percent coupon rate and semiannual interest payments. Here's how to calculate the bond's price:
- Calculate the periodic interest rate by dividing the annual market interest rate by the number of periods per year. In this case, the market interest rate is 10.2 percent, so the periodic interest rate is 10.2% / 2 = 5.1%.
- Calculate the number of periods by multiplying the number of years left to maturity by the number of periods per year. In this case, there are 10 years left to maturity and 2 periods per year, so there are 10 * 2 = 20 periods.
- Calculate the present value of the coupon payments. Each coupon payment is $1,000 * (6.2% / 2) = $31, and the present value of these payments can be calculated using the formula for the present value of an annuity. In this case, the periodic interest rate is 5.1%, the number of periods is 20, and the coupon payment is $31. Substituting these values into the formula, the present value of the coupon payments is $31 * (1 - (1 + 5.1%)^(-20)) / 5.1% = $527.08.
- Calculate the present value of the final principal payment. The final principal payment is $1,000, and its present value is $1,000 / (1 + 5.1%)^20 = $328.42.
- Calculate the total present value of the bond by summing the present value of the coupon payments and the present value of the final principal payment. In this case, the total present value is $527.08 + $328.42 = $855.50.
Therefore, the price of the bond is $855.50.