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Appendix E: Monthly and Continuous Discount Rates Theexamplesinthismanualhaveassumedend-of-yearcashflowsandannualdiscountrates. However, it is not uncommon for cash flows to occur during or at the beginning of the month, and it is not uncommon for discount rates and interest rates to be stated in s e m i - m u d , monthly, or even continuous values. For example, if a bank pays 8% interest compounded quarterly, this means that the nominal annual interest rateis8%andthequarterlyinterestrateis2%. Inthisexample,theinvestorwouldreceive2%interest ontheprincipalattheendofeachquarter. Aneffectiveannualinterestrateistheinterestratethat,when applied once per year to a principal sum, will give the same amount of interest equal to a nominal rate of r% per year compounded n times per year. The formula for calculation of the effective interest rate is: Where: re = r = n = effective annual interest rate nominal annual interest rate number of compounding periods per year. If the number of compounding periods is infinite, the formula for calculating effective interest becomes: For example, assuming a nominal interest rate of 12%, the effective interest rate is as follows: 1. When compounded quarterly it is (1 + 0.12/4>"= 12.55% 2. When compounded monthly it is (1 + 0.12/12)12= 12.68% 3. When compounded daily it is (1 +0.12/365)365= 12.747% 4. When compounded continuously it is (eoP1'- 1) = 12.749%. As one can see from this example, the more frequently interest is compounded, the greater the effective interest rate. Although it is uncommon, analyses sometimes account for cash flows that occur at times other than the endoftheyear. InthePresentValuesubsectioninSection2,thefollowingexamplewasputforth. Cash flows of $1 and $5 are assumed to occur at the end of periods 1 and 2 and are discounted at a rate of 5%. The calculated present value of the cash flows is $5.49, as shown in Table E-1. E-1PDF Image | A Manual for the Economic Evaluation of Energy Efficiency and Renewable Energy Technologies
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