TABLE OF CONTENTS At various points, the notation PV [ r, ?] appears. This function is the conventional present value discounting operator for a cash flow of $1 to be received in ? = T ? t days. In Chapter 7, Section I, this is defined as the present value at time t of $1 to be received at time T. PV[ ?] means the present value evaluated at ? = T ? t. This can be evaluated using either a continuous or discrete formulation. In order to reduce the amount of notation, PV [ ?] is used to represent both continuous and discrete compounding, even though there are slight differences in the two cases. However, with correct specification of the interest rates used in the discounting process, results of the continuous and discrete compounding operations are identical.
In discrete time, the discounting operator takes the linear form, 1/(1 + rt*), when t* is less than 1, and 1/(1 + r) t* where t* is an integer greater than zero. The geometric form of the discounting operator, 1/(1 + r) t*, is also encountered where t* can take any value. For both these cases, r is expressed as an annualized interest rate. In continuous time, the discounting operator takes the form, exp{ ? rt*} ? e ? rt* where r
