Final answer:
Yield-to-maturity (YTM) of a bond is calculated using a formula that takes into account the bond's current price, future cash flows from coupon payments, and face value at maturity. A financial calculator is typically required for precise calculations, as the formula involves solving for YTM for which the present value of future cash flows equals the bond's current price. Based on given options, the closest answer would be selected as the bond's YTM.
Step-by-step explanation:
Calculating Yield-to-Maturity on a Bond
To calculate the yield-to-maturity (YTM) for a bond, we must consider the current price, face value, coupon payments, and time to maturity. The bond in question has a face value of $1,000, a semi-annual coupon rate of 7%, matures in 2 years, and is currently selling at a price of $997.07. Given that the coupon payments are made semi-annually, we would receive $35 every six months for the next two years, plus the face value at maturity.
To find the YTM, we would use the following formula to equate the present value of future cash flows from the bond to its current price:
Current Price = C [(1 - (1 + YTM)-n) / YTM] + FV / (1 + YTM)n
Where:
- C is the semi-annual coupon payment ($35)
- YTM is the yield-to-maturity
- n is the number of semi-annual periods (4)
- FV is the face value of the bond ($1,000)
This calculation would typically be solved using a financial calculator or software that is designed for solving such equations. You would input the values and solve for the YTM that equates the present value of future cash flows to the current bond price of $997.07.
Without the financial calculator, we cannot provide the exact YTM but based on the choices provided, the correct answer is the one that comes closest to satisfying the YTM formula when plugged in.