Interest periods

Materials chemistry is now served by a whole range of journals, ranging from the venerable Journal of Solid-State Chemistry and Materials Researeh Bulletin (already mentioned) to Materials Chemistry and Physies (which, interestingly, now incorporates The International Journal of the Chinese Soeiety for Materials Seienee... which appears to be distinct from the Chinese MRS) and Journal of Materials Chemistry (published by the RSC in London) - also Chemistry of Materials, published by the ACS. In France, Annales de Chimie Seienee des Materiaux is an offshoot of a journal originally founded by Lavoisier in 1789 (shortly before he lost his head). Journal of Materials Synthesis and Proeessing is an interesting periodical with somewhat narrower focus. 

Simulations of water in synthetic and biological membranes are often performed by modeling the pore as an approximately cylindrical tube of infinite length (thus employing periodic boundary conditions in one direction only). Such a system contains one (curved) interface between the aqueous phase and the pore surface. If the entrance region of the channel is important, or if the pore is to be simulated in equilibrium with a bulk-like phase, a scheme like the one in Fig. 2 can be used. In such a system there are two planar interfaces (with a hole representing the channel entrance) in addition to the curved interface of interest. Periodic boundary conditions can be applied again in all three directions of space. 

Compound interest was used in the above case. Compound interest means that the interest earned is figured not only on the principal but also on any previously earned interest. This is equivalent to increasing the principal by the amount of interest after each interest period. See Table 10-3 for the development of the following simple formula for compound interest. ... 

Period Principal Earnings at Beginning of Interest Period Interest at End of Interest Period... 

Periodic acid reacts well in aqueous solution. Usually, if the reactant has to be run in organic solvents, lead tetraacetate is used as the reagent. Interestingly, periodic acid will not act on a-keto acids or a-hydroxy acids whereas lead tetraacetate wiU. The corresponding reactions are actually oxidative decarboxylations. 

C Cost of equipment m Number of interest periods Varies... 

Continuous compounding A mathematical procedure for evaluating compound interest based upon continuous interest function rather than discrete interest periods. 

Most public libraries subscribe to database services such as InfoTrac or EBSCO that index articles from hundreds of general-interest periodicals (and some moderately specialized ones). The database can be searched by author or by words in the title, subject headings, and sometimes words found anywhere in the article text. Depending on the database used, hits in the database can result in just a bibliographical description (author, tide, pages, periodical name, issue date), a description plus an abstract (a paragraph summarizing the contents of the article), or the full text of the article itself. 

Another interesting periodic trend is density. Osmium, Os (atomic number 76), has the greatest density of all elements, and, with some exceptions, the closer an element is to osmium in the periodic table, the greater its density. Use this trend to list the following elements in order of increasing density copper, Cu gold, Au platinum, Pt and silver, Ag ... 

If P represents the principal, n the number of time units or interest periods, and i the interest rate based on the length of one interest period, the amount of simple interest Z during n interest periods is... 

The principal must be repaid eventually therefore, the entire amount S of principal plus simple interest due after n interest periods is... 

The time unit used to determine the number of interest periods is usually 1 year, and the interest rate is expressed on a yearly basis. When an interest period of less than 1 year is involved, the ordinary way to determine simple interest is to assume the year consists of twelve 30-day months, or 360 days. The exact method accounts for the fact that there are 365 days in a normal year. Thus, if the interest rate is expressed on the regular yearly basis and d represents the number of days in an interest period, the following relationships apply ... 

The compound amount due after any discrete number of interest periods can be determined as follows ... 

Therefore, the total amount of principal plus compounded interest due after n interest periods and designated as S isf... 

The term (1 + i)" is commonly referred to as the discrete single-payment compound-amount factor. Values for this factor at various interest rates and numbers of interest periods are given in Table 1. 

In common industrial practice, the length of the discrete interest period is assumed to be 1 year and the fixed interest rate i is based on 1 year. However, there are cases where other time units are employed. Even though the actual interest period is not 1 year, the interest rate is often expressed on an annual basis. Consider an example in which the interest rate is 3 percent per period... 

In this equation, S represents the total amount of principal plus interest due after n periods at the periodic interest rate i. Let r be the nominal interest rate under conditions where there are m conversions or interest periods per year. 

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. 

Equations (6), (7), and (8) represent the basic expressions from which continuous-interest relationships can be developed. The symbol r represents the nominal interest rate with m interest periods per year. If the interest is compounded continuously, m approaches infinity, and Eq. (6) can be written as... 

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). 

The common type of annuity involves payments which occur at the end of each interest period This is known as an ordinary annuity. Interest is paid on all accumulated amounts, and the interest is compounded each payment period. An annuity term is the time from the beginning of the first payment period to the end of the last payment period. The amount of an annuity is the sum of all the payments plus interest if allowed to accumulate at a definite rate of interest from the time of initial payment to the end of the annuity term. 

As before, let r represent the nominal interest rate with m conversions or interest periods per year so that i = r/m and the total number of interest... 

In a perpetuity, such as in the preceding example, the amount required for the replacement must be earned as compounded interest over a given length of time. Let Pbe the amount of present principal (i.e., the present worth) which can accumulate to an amount of S during n interest periods at periodic interest rate i. Then, by Eq. (5),... 

The end-of-year convention is normally adopted for discrete interest factors (or for lump-sum payments) wherein the time unit of one interest period is assumed to be one year with interest compounding (or with lump-sum payments being made) at the end of each period. Thus, the effective interest rate is the form of interest most commonly understood and used by management and business executives. 

C = compound interest factor CR = cost for replacement or other asset, dollars Cv = original cost of equipment or other asset, dollars d = number of days in an interest period, days, or derivative e = base of the natural logarithm = 2.71828... ... 

Z = total amount of interest during n interest periods, dollars K = capitalized cost, dollars m = number of interest periods per year n = number of time units or interest periods... 

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