Before we delve into all the good stuff (swaps and options), let us review some fixed income basics.

Following the classical fixed income gospels, we remember that the *Future Value*, *FV*, on a horizon date of an investment *PV* at an annual interest rate of *r* , *compounded m* times a year, for *N* whole compounding periods is

For example, if *m* = 1, we have annual compounding *FV* = *PV*(1 + *r* )^{N}, and N is the number of years until the future horizon date. If *m* = 2, we have semiannual compounding (standard for U.S. Treasury securities) *FV* = *PV*(1 + *r /*2)^{N}, and *N* = 2*T* is the number of whole semiannual periods until the horizon date (*T* years from now).

The above formula can be easily generalized to incorporate horizon dates that are not a whole number of compounding periods away. We compute *T* as the number of years between the investment date and the horizon date, according to some day count basis, and come up with:

From college math courses, we recall that as you increase the compounding frequency, the above, in the limit, becomes
and *r* is then referred to as the *continuous* compounding rate.

An alternative to using compounded rates is to use *simple* or noncompounding interest rates:

where *T* is the number of years (can be fractional) to the horizon ...

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