Question

A U.S. Treasury bond pays a 4.5% coupon rate, has a $1,000 par value, and matures 30 years from now in 2050. The bond’s bid quote is 116:10 and the ask quote is 116:12. Coupon payments are semiannual. If you purchase this bond now and hold it until 2050, what would be your annual yield to maturity?

Answer 1

yield of maturity =3.60 %

Step-by-step explanation:

given data

face value FV = $1000

coupon rate r = 4.5%

no of compounding peryear = 2

time period t = 30 year

solution

first we get here interest per period that is PMT

PMT = FV × r ÷ 2

PMT = 1000 × 4.5% ÷ 2 = 23

now we get here bond value that is

bond value = 1000 × (116 +
`(12)/(32)` )%

bond value = 1163.75

and

number of compound period till the maturity will be NPER

NPER = no of compounding peryear × time period

NPER = 30 × 2 = 60

so now we get here yield of maturity by excel formula that is

yield of maturity = RATE(NPER,PMT,-PV,FV) × 2

yield of maturity = RATE(60,22.5,-1163.75,1000) × 2

yield of maturity =3.60 %