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Discounting Using Spot Rates

There are plenty of excellent treatments of the term structure. I therefore keep this chapter short and to the point. The yield curve is a plot of Treasury spot rates. The spot rate is the current market interest rate for a given term (for example, the yield on the one-year Treasury bill). For example, lending $1 at 10 percent for a single year means that the one-year spot rate is 0.10. If you were to lend the $1 for a period of two years at 10 percent annually, then the two-year spot rate is also 0.10. So, for the one-year spot, s₁, and a $1 investment, the factor by which that investment will grow is . For the same $1, over two years, that investment will grow to , or 100^∗s₂ percent in each of two years. In general, then, $1 will grow at for a period of t years at an annual rate equal to s_t. If the rate is compounded m times per year, then this changes to: . And, if the rate is compounded continuously, then as we have shown before, , where the second time ...