Final answer:
To determine the years until a bond's maturity, one needs to calculate the number of periods based on the bond pricing formula, accounting for the yield to maturity, coupon rate, current bond price, and face value. This requires a financial calculator or software as the calculation can be quite complex.
Step-by-step explanation:
The student is asking how to calculate the time until maturity for a semiannual coupon bond with given financial parameters. Given the yield to maturity (YTM) of 12.80%, a coupon rate of 11%, the current bond price of $863.75, and the face value of $1,000. The calculation of the maturity involves the time value of money concepts where the present value of expected cash flows (coupons plus the face value at maturity) equals the current bond price.
The bond makes semiannual payments of $(1000 * 0.11) / 2 = $55. To find the number of years until maturity, one can use the bond pricing formula and solve for the number of periods (n). This involves a financial calculator or solving iteratively or with financial software as it's a complex present value calculation. It's important to remember that the final cash flow will include both the last interest payment and the bond's face value.
Interest rates and bond prices have an inverse relationship. When interest rates rise, the price of existing bonds falls to increase the yield and make them competitive in the market, and vice versa when interest rates fall.