Interest discrete compounding

Figure 7-1 shows a comparison among the total amounts due at different times for the cases where simple interest, discrete compound interest, and continuous interest are used. 

Discrete Compound Interest In financial transactions, loans or deposits are made using compound interest. The interest is not withdrawn but is added to the principal for that time period. In the next time period, the interest is calculated upon the principal plus the interest from the preceding time period. This process illustrates compound interest. In equation format,... 

Interest calculated for a given time period is known as discrete compound interest, with discrete referring to a discrete time period. Table 9-21 contains 5 and 6 percent discrete interest factors. 

The numerical difference between discrete compound interest and continuous compound interest is small, but when large sums of money are involved, the difference may be significant. Table 9-23 is an abbreviated continuous interest table, assuming that time zero is when start-up occurs. A summary of the equations for discrete compound and continuous compound interest is found in Table 9-24. 

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. 

Discrete compound-interest factor (1 + i)H at various values of i and rtf... 

The preceding discussion of types of interest has considered only the common form of interest in which the payments are charged at periodic and discrete intervals, where the intervals represent a finite length of time with interest accumulating in a discrete amount at the end of each interest period. Although in practice the basic time interval for interest accumulation is usually taken as one year, shorter time periods can be used as, for example, one month, one day, one hour, or one second. The extreme case, of course, is when the time interval becomes infinitesimally small so that the interest is compounded continuously. 

In Eq. (5), S represents the amouht available after n interest periods if the initial principal is P and the discrete compound-interest rate is i. Therefore, the present worth can be determined by merely rearranging Eq. (5). 

Example 4 Determination of present worth and discount. A bond has a maturity value of 1000 and is paying discrete compound interest at an effective annual rate of 3 percent. Determine the following at a time four years before the bond reaches maturity value ... 

The discrete compounds containing single boron atoms or single metal atoms are about as far from systems having metallic character as it is possible to get. Hence, the purpose of this section is to simply draw the readers attention to some interesting similarities between the chemistry of boron and a transition metal. One of the characteristic chemistries associated with transition metals is that of ligand coordination, and we present comparisons between a few boron and metal coordination compounds below. Even for these covalent species, the selected compounds illustrate and support the theme of this chapter. 

We have seen how bonding principles carry over from discrete species to related fragments in the solid state. An interesting question then is whether the same discrete species can serve as precursors for the efficient production of specific solid state materials containing the cluster cores of the discrete compounds as building blocks of the solid. 

Compound Interest Factors Discrete Cash Flow, Discrete Compounding 2.4.1. Compound Amount Factor (Single Payment)... 

Compound Interest Factors Discrete Cash Flow, Discrete 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. 

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. 

DISCRETE COMPOUND INTEREST FACTORS Interest Rate 10%... 

GEOMETRIC SERIES FACTORS DISCRETE COMPOUNDING FUTURE WORTH FACTOR F/A Interest Rate 15%... 

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