Bonds often pay a coupon twice a year. For the valuation of bonds that make semiannual payments, the number of periods doubles, whereas the amount of cash flow decreases by half. Using the values of cash flows and number of periods, the valuation model is adjusted accordingly.

Assume that a $$1,000,000$ par value, semiannual coupon US Treasury note with four years to maturity has a coupon rate of $4\%.$ The yield to maturity $($YTM$)$ of the bond is $7\mathrm{.}70\%.$ Using this information and ignoring the other costs involved, calculate the value of the Treasury note:

$$874,669\mathrm{.}10$

$$551,041\mathrm{.}53$

$$743,468\mathrm{.}74$

$$1,049,602\mathrm{.}92$