Final answer:
The question pertains to Business and involves calculating the price of a Zero Coupon Bond at different yields to maturity (YTM). It includes discounting the face value to present value considering semiannual compounding and requires understanding of the relationship between bond prices and interest rates.
Step-by-step explanation:
The subject of the question is Business specifically focusing on the valuation of Zero Coupon Bonds and how their prices are affected by the yield to maturity (YTM). The grade level is College, as it entails financial concepts and calculations that are typically covered at the undergraduate or graduate level in finance or business courses. To find the price of a Zero Coupon Bond for different YTMs we use the present value formula. Since Zero Coupon Bonds do not pay periodic interest (coupon), their price is determined by discounting the face value of the bond back to the present value using the YTM as the discount rate, taking into account the number of compounding periods (semiannual). For example, if a bond with a face value of $1,000 and 10 years to maturity has YTMs of 5%, 10%, and 15%, the prices would be calculated using the formula: Price = Face Value / (1 + r/n)^(nt), where r is the YTM, n is the number of compounding periods per year, and t is the number of years. Remember, when interest rates rise, the price of existing bonds typically falls, resulting in a higher yield to the purchaser, and vice versa.