# Formula to compute 10 year US governement bond price given yield

What is the formula to convert US govy 10 year yields (as those shown here) in to bond prices?

I know in general the math looks like this but I don't know what the values of the variables are for a plain vanilla US 10 year govy paper (# of coupons, pay out at maturity ect)

## 1 Answer

Treasury Direct tells us:

• Treasury bonds are interest-bearing securities with maturities over 10 years.
• Treasury bonds pay interest on a semi-annual basis.
• When a bond matures, the investor receives the face value.

A 10 year US treasury bond has 20 coupons and pays face value at maturity. Were there other variables you needed?

• I can't vote (too low reps) but I have a further question: If r is the annual yield, to get the the semi-annual yield, do you just divide the annual yield in by (i.e. (1+r/2)) , or do you do sqrt((1+r)). The web site I linked to says the former, but the latter seems more logical (interests compound!) – user42397 Sep 13 '15 at 9:50
• @user42397 Bonds are quoted based on the periodic interest rate times the number of payments in a year, not the true "annualized" interest rate, so dividing the quoted rate by 2 is appropriate to find the periodic rate for a semi-annual bond. – D Stanley May 14 '18 at 13:25