Question

In February 2015 Treasury 3 7/8s of 2037 offered a semiannually compounded yield to maturity of 2.94%. Recognizing that coupons are paid semiannually, calculate the bond's price. Assume face value is $1,000.

Answer 1

Bond Valuation: The value of bond is the present value of the expected cashflows from the bond,discounted at Yield to Maturity(YTM).

Years remaining to maturity = 2037-2015 = 22 years

Interest rate = ((3*8)+7)/8 = 3.875%

Year	Cash flow	PVAF/[email protected]%	Present Value (Cashflow*PVAF/PVF)
1-44	19.375	32.2319	624.49
44	1000	0.5262	526.19

Price of Bonds = $\sum$Cashflow*PVAF/PVF

= 624.49+526.19

= 1150.68

Note : Since the bond makes semiannual interest payments, total no. of period is 44 (22*2), cashflow per period is 19.375(1000*3.875%/2) and cashflows are discounted at 1.47%(2.94/2)

note: It is general practice to take $1,000 as face value when no details are given