Continuous compound interest factors

CONTINUOUS COMPOUNDING INTEREST FACTORS Interest Rate 9%... 

Compound Interest Factors Continuous Uniform Cash Rows, Continuous... 

Compound Interest Factors Discrete Cash Flow, Continuous Compounding... 

The limit of (1 + Mk f as k approaches infinity is e. Thus, Eq. (2) can be written as and the single-payment continuous compounding amount factor at r% nominal annual interest rate for N years is Also, since (for continuous compounding) corresponds to (1 + i) for discrete compounding,... 

By the use of this relationship, the compound interest factors for discrete cash flows compound continuously shown in Table 1 can be derived from the discrete compounding factors in Table 2. 

In (1.6) e" is the exponentialfunction of rn. It represents the continuously compounded interest rate factor. To compute this factor for an interest rate of 6 percent over a term of one year, set r to 6 percent and to 1, giving... 

Expression (3.13) states that the bond price is a function of the continuously compounded interest rate. The r ht-hand side is the discount factor at time t. At t= T—that is, on the redemption date—the discount factor is 1, which is the redemption value of the bond and hence the price of the bond at that time. 

Tables of interest and cash-flow factors, such as are illustrated in Tables 1, 5, 6, 7, and 8 of this chapter, are presented in all standard interest handbooks and textbooks on the mathematics of finance as well as in appendices of most textbooks on engineering economy. Exponential functions for continuous compounding are available in the standard mathematical tables. The development of tables for any of the specialized factors is a relatively simple matter with the ready availability of digital computers, as is illustrated in Example 3 of this chapter.

This factor is used to find the equivalent future worth, F, of a present value, P, when the interest is continuously compounded at the nominal annual rate of r%. For example, consider the problem of finding the future worth in six years of 5,000 invested now at 9% nominal interest rate compounded continuously. 

Note that the only difference between continuous compounding and discrete compounding in finding equivalent values of F, P, A, and G is the interest factor used (r, the nominal annual interest rate). Consequently, to solve discrete cash flow continuous compounding problems, use the same proeedures illustrated for discrete compounding with the functional format. 

Again, as with discrete cash flows, to solve for one variable given another, it is only necessary to select the proper interest factor for continuous cash flow, continuous compounding. A listing of these factors can be found in Table 3. 

CONTINUOUS COMPOUNDING CONTINUOUS FLOW FACTORS Interest Rate 15%... 

The factor, ——, is referred to as the continuous uniform-series compound-amount factor. Equation (17,30) seems hypothetical because, although interest can be credited continuously, payments cannot be made continuously. 

Cyclic ureas incorporating a 1,3-diazepinone skeleton continue to be of pharmacological interest. The Ai V-disubstituted system 89 has been prepared and shown to be a potent inhibitor of factor Xa in vitro and to have an improved pharmacokinetic profile in the rabbit. The binding model for this series of compounds was confirmed by an X-ray crystallographic analysis of one analogue in the series <00BMCL301>. 

Income after startup. The business income is normally spread throughout the year, and a realistic interpretation is that 1/365 of the annual earnings is being received at the end of each day. The present-worth factors for this type of incremental income are essentially equal to the continuous-income present-worth factors. Even though the present worth of the income should be computed on a continuous-income basis, it is a matter of individual policy as to whether continuous or discrete compounding of interest is used. The income for each year can be converted to the reference point by the appropriate equation. 

For profitability analyses, certain discounting or compounding factors based on continuous interest compounding are of sufficient importance that tables have been prepared which give values of the factors for various interest rates and time periods. Table 3 gives examples of tabulated factors for the following cases t ... 

Discount and compounding factors for continuous interest and cash flows ... 

In the tabulation of factors for continuous interest compounding and continuous cash flow, the nominal interest rate r is used for calculating the... 

Example 2 Discounted-cash-flow calculations based on continuous interest compounding and continuous cash Row. Using the discount factors for continuous interest and continuous cash flow presented in Tables 5 to 8 of Chapter 7, determine the continuous discounted-cash-flow rate of return r for the example presented in the preceding section where yearly cash flow is continuous. The data follow. 

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