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 7.70%. Using this information and ignoring the other costs involved, calculate the value of the Treasury note: $874,669.10 $551,041.53 $743,468.74 $1,049,602.92

Explanation:

the present value of the future cash flows is the the value of the bond we calculate the present value as follows

Cash flow  4% = 40000 per year for 4 year p.v using annuity

Cash flow = 1000000 at year four present value using compound formula

Present value at yield rate 7.7%

Cash flowDiscount FactorPresent Value

10000000.743253883           743253.8831

40000         3.334365155           133374.6062

                                            876628.4893

Compound = 1000000/(1+7.7%)^4

Annuity       = 40000*  (1-(1+7.7%)^-4) / 7.7%

you have to put the parentheses like this:

in fact, you have to perform the operation inside parentheses first, and then proceed in order: