question There is a zero coupon bond that sells for $393

Zero coupon bond does not pay any coupon payments during the life of the bond. The price of a bond is equal to present value of all the future cash flows that come from it. For a zero coupon bond, the present value of face value would be equal to the price. The discounting would be done using the yield to maturity.

As semi-annual compounding is present, the time period becomes 16*2 = 32 six monthly periods. Let the effective yield for 6 months be YTM

Therefore for a zero coupon bond, the price = Face value/(1+YTM)^periods

393.78 = 1000/(1+YTM)^32

(1+YTM)^32 = 2.539489

YTM = 0.029552

This is the effective yield for six monthly periods.

Thus, the in annual terms, the Yield to Maturity will be 0.029552*2 = 0.059104 or 5.91%.

Thus, the required yield to maturity is 5.91%.