Final answer:
The yield-to-maturity (YTM) on a 15-year, zero-coupon bond with a face value of $1,000 and a current price of $331.40, considering semiannual compounding, is approximately 5.151%.
Step-by-step explanation:
Based on semiannual compounding, to calculate the yield-to-maturity (YTM) on a 15-year, zero-coupon, $1,000 par value bond currently trading at $331.40, we can use the formula for YTM which equates the present value of future cash flows to the current price of the bond.
We know that the future value (FV) is $1,000, the present value (PV) is $331.40, the number of periods (n) is 15 years with semiannual compounding, so it would be 15 * 2 = 30 periods, and the payment (PMT) is $0 since it's a zero-coupon bond. The equation for YTM in this case can be represented as PV = FV / (1 + YTM/2)^(2*n). To find the YTM, we would need to solve for the interest rate that makes the equation true.
After solving this equation using either a financial calculator, an equation-solving tool, or an iterative process, you will find that the correct YTM closely matches with option B, which is 5.151%.