So there's one more complication to think about, and that is the fact that corporations in the US government don't issue annual bonds. They issue semi-annual bonds. So a semi-annual bond has cashflows that look like this. The first cashflow you receive six months after you buy the bond. The way semi-annual bonds are quoted, they don't quote you the semi-annual coupon, they quote you an annual coupon. So in the first six months, you receive the coupon divided by two. After the next six months, you receive the coupon divided by two. At a year and six months, you receive the coupon divided by two, and so on and so forth every six months until the maturity when you receive the face value plus the coupon divided by two. Now to make everything even and to work out really nicely, the yield to maturity on a semi-annual bond is a stated annual interest rate. So the price is C over 2 divided by 1 plus r_a over 2. Remember that we use the notation r_a to denote a state at annual interest rate. So this is the first payment which is at the six month mark. This is the second payment, which is at the one-year mark, and the third payment, one year and six months, and so on and so forth the last payment which we raise the 1 plus r_a over 2 to the 2t. Notice that for each of these pieces, we are doing what is in effect an effective annual rate calculation. The effective annual rate for this bond is 1 plus r_a over 2 squared minus 1. So it's as if there's a little effective annual rate calculation happening at each of these pieces. So we're just going to do one example, just to be super crystal-clear. Example, semi-annual bond, coupon rate of eight percent, yield to maturity of eight percent, maturity of 10 years, selling for a face value of $1,000. The price of this bond is equal to 40 over 1.04 plus 40 over 1.04 squared plus 40 over 1.04 cubed plus dot dot dot plus 1,040 over 1.04 to the 20. So notice, here the yield to maturity is a stated annual interest rate of eight percent. My period rate is my stated annual interest rate over two, the period is two. That's four percent. Now the effective annual rate on this bond is 1.04 squared minus 1, which is 8.16 percent. Now why do we go through this whole mess of stating the yield to maturity as a stated annual interest rate? Well it has one very desirable feature. If you stare at this formula long enough, you'll notice that you really couldn't tell the difference between a semi-annual bond with a yield to maturity of eight percent, coupon rate of eight percent, and a maturity of 10 years, and an annual bond with a yield to maturity of four percent and a coupon rate of four percent, and a maturity of 20 years. They actually look the same. They're what you might call isomorphic, and so all the nice relations that we had for an annual bond continue to be true for a semi-annual bond. Namely, for a semi-annual bond, the price is equal to the face value, if and only if the yield to maturity equals the coupon rate. A statement that would only be true if the yield to maturity was quoted as a stated annual interest rate. We have our other relations too. The bond sells at a premium if the yield to maturity is less than the coupon rate, and the bond sells at a discount if the yield to maturity is greater than the coupon rate, same as for an annual bond. That's it for semi-annual bonds.