Valuing semiannual coupon bonds

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:

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

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

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

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

Based on your calculations and understanding of semiannual coupon bonds, complete the following statement:

When valuing a semiannual coupon bond, the time period variable $(N)$ used to calculate the price of a bond reflects the number of

periods remaining in the bond's life.