Final answer:
The yield to maturity of a bond with an 8 percent coupon rate and a current price of $878.31 is found by calculating the rate of return that equates the present value of future cash flows to the bond's current price. Using process of elimination, the closest answer is 10 percent, corresponding to choice (d).
Step-by-step explanation:
To calculate the yield to maturity of a bond, we determine the rate of return that makes the present value of all future cash flows equal to the current price of the bond. For a bond with an 8 percent coupon rate, an annual interest payment would be $80 (8% of the $1,000 face value). Over four years, you will receive a total of $320 in interest payments (4 x $80). At maturity, you receive the face value of $1,000. To find the yield to maturity, we need to find the rate that equates the present value of these cash flows ($80 per year for four years, plus the $1,000 face value) to the current price of the bond, which is $878.31.
The formula to calculate present value is:
PV = ∑ [C / (1 + r)^t] + [FV / (1 + r)^n]
Where:
- PV is the present value or current price of the bond
- C is the annual coupon payment ($80)
- r is the yield to maturity (what we are solving for)
- t is the time in years until the payment is received
- FV is the face value of the bond ($1,000)
- n is the number of years until maturity
To solve for the yield to maturity, you would typically use financial calculator or spreadsheet software to find the rate that makes the present value of the cash flows equal to $878.31.
However, based on the provided potential answers, we can use the process of elimination or trial and error with the given options. Using this approach, we calculate the yield to maturity as 10 percent, because it is the rate that comes closest to making the present value of the future cash flows equal to the current price of $878.31. Therefore, the correct option is d. 10 percent.