Final answer:
The yield-to-maturity (YTM) considers both coupon payments and capital gains or losses on a bond if held to maturity. Calculating YTM accurately requires a financial calculator or software and is based on the bond's coupon rate, face value, and purchase price in relation to its face value. YTM fluctuates with market interest rates, affecting the bond’s price and overall return.
Step-by-step explanation:
The yield-to-maturity (YTM) of a bond is a calculation of the total expected return on a bond if the bond is held until maturity, comprising both the bond's coupon payments and any capital gains or losses (if the bond was purchased at a discount or premium to its face value). Given that Gwenyth purchased a bond with a 13.13% coupon interest rate paid annually and a purchase price of $1,043, we need to calculate the yield based on the annual coupon payment that she will receive, the face value of the bond at maturity, and what she paid for it. The bond has a face value of $1,000, so until maturity, Gwenyth will receive 13.13% of that amount each year. At the end of the bond's life, she will receive the face value of $1,000. The YTM formula typically incorporates the present value of all future cash flows (interest payments and the face value at maturity) and the current price of the bond to solve for the yield.
Calculating YTM can be done using a financial calculator or software capable of solving for the internal rate of return (IRR). This considers the present value of the face value, the present value of the coupon payments, and the current bond price. However, because YTM calculations are beyond the scope of simple algebra and require iterative methods or financial calculators, we'll not provide an exact YTM figure here.
It is important to note that if the interest rates in the market rise, the price of existing bonds falls, as new bonds might be issued with higher coupon rates, making older bonds less attractive. Conversely, if the interest rates fall, the price of existing bonds rises, as they pay higher interest compared to new bonds. Since the coupon rate on Gwenyth's bond did not change, the relationship between the bond's price and market interest rates will influence its YTM.