Question

A Treasury bond that settles on August 10, 2016, matures on February 23, 2024. The coupon rate is 7.0 percent and the quoted price is 117:15. What is the bond’s yield to maturity?

yield to maturity?

Answer 1

Answer :

Assuming that the face value ( F ) = $1,000

Given that, Coupon rate = 7.0%

Quoted price = 117:15

So, it means 117 + 15 / 32 = 117.46875

And P = 1,000 * 117.46875% = $ 1,174.69

Number of years = 7 + 196 / 365 = 7.54

Coupon payment , I = 0.07 * 1,000 = 70

Using YTM approximation formula , we get

YTM = [ I + ( F - P ) / n ] / ( F + P ) / 2

YTM = [ 70 + ( 1,000 - 1,174.69 ) / 7.54 ] / ( 1,000 + 1,174.69 ) / 2

YTM = [ 70 + ( -23.17 ) ] / 1087.345

YTM = 0.0431 = 4.31%

Therefore, Yield to maturity is 4.31%.