So let's think about a bond that has a face value of $1,000, a maturity of five years, and also that the interest rate is seven percent. What's the price of this bond? Well, we're going to use present value. So we take our face value and we discounted back five years at an interest rate of seven percent. That gives us $712.99. Now, why is this bond worth $712.99? Is it just because the formula says it should be worth that? Well, no. It all comes down to the fact that this r is seven percent, which is telling us the time value of money. If, for example, the price were bigger than $712.99, presumably nobody would buy the bond. You would earn more putting your money for five years in the bank. If the price was less than $712.99, everybody would be trying to buy the bond, perhaps using borrowed money. In either case, the bond dealers would be forced to adjust the price to maintain their inventory. So market forces are what's going to send this price back to be $712.99. So now let's think about this example a little bit more. Again, we'll keep the interest rate, R, at seven percent. So if we have a maturity of five years, the price is $712.99. If instead the maturity is three years, well, we can do the same present value calculation. It's, by the way, 1,000 over 1.07 cubed, and that gives us $816.30. Now, the thing about bonds is we can see these numbers as two different bonds at the same point in time. So at a single point in time, there might be a five-year bond and a three-year bond, or the same bond at two different points in time. So the five-year bond selling for a price of $712.99, assuming market conditions don't change, two years later becomes a bond selling for $816.30. Then three years after that, so of a maturity of zero years, the bond, of course, is going to be worth its face value of $1,000. So some people call this process that the bond is being pulled to par. Par being another word for face value. So the idea is that there's a force pulling the bond price to its par value of $1,000. Well, that force is really nothing other than the time value of money. So now let's ask a different question. Given a price, and of course, a face value, what r makes this price correct? So let's say we start with a price of $712.99. So now we can solve for r. Well, we get price equals face value discounted back in this case by five years. So $712.99 equals $1,000 over 1 plus r to the fifth. Well, that implies that we already know r equals seven percent. In general, we can solve for R. P equals F over 1 plus r to the t. Doing a bit of algebra, p times 1 plus r to the t equals f. 1 plus r to the t equals F over P, and finally, r equals F over P to the 1 over t minus 1. When we solve for the R, that makes the price equal to the present value. That r has a specific name. This is called the yield to maturity.