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FINC 322 - Chapter 6 Continuous Compounding

FINC 322 - Chapter 6 Continuous Compounding - integral of...

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FINC 322 Financial Management 1 Chapter 6 Supplementary Note 1 Continuous compounding Rates are sometimes converted into the continuous compound interest rate equivalent because the continuous equivalent is more convenient (for example, more easily differentiated). Each of the formulæ above may be restated in their continuous equivalents. For example, the present value at time 0 of a future payment at time t can be restated in the following way, where e is the base of the natural logarithm and r is the continuously compounded rate: This can be generalized to discount rates that vary over time: instead of a constant discount rate r, one uses a function of time r ( t ). In that case the discount factor, and thus the present value, of a cash flow at time T is given by the
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Unformatted text preview: integral of the continuously compounded rate r ( t ): Indeed, a key reason for using continuous compounding is to simplify the analysis of varying discount rates and to allow one to use the tools of calculus. Further, for interest accrued and capitalized overnight (hence compounded daily), continuous compounding is a close approximation for the actual daily compounding. More sophisticated analysis includes the use of differential equations , as detailed below. Examples Using continuous compounding yields the following formulas for various instruments: Annuity Perpetuity Growing annuity Growing perpetuity • FV for ordinary annuity and growing annuity can be calculated by Source: http://en.wikipedia.org/wiki/Time_value_of_money...
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