Interest compound

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 The interest is not withdrawn but is added to the principal for that time period.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, 

Future sum Future value Future worth Future amount Principal Present worth Present value Present amount 

An interest rate quoted on an annual basis is called nominal interest. However, interest may be payable on a semiannual, quarterly monthly, or daily basis. To determine the amount compounded, the following equation applies  

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. 

Examples of the use of discrete factors for various applications are found in Table 9-22, assuming that the present time is when the first funds are expended. 

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Suppose you have to meet an obligation to pay a bill of 10,000 in 5 years time. If you could be guaranteed a compound interest rate in your bank of 7% per annum (after tax) over each of the next 5 years, then the sum which you would have to invest today to be able to meet the obligation in 5 years time would be ... 

In the above example, the discount rate used was the annual compound interest rate offered by the bank. In business investment opportunities the appropriate discount rate is the cost of capital to the company. This may be calculated in different ways, but should always reflect how much it costs the oil company to borrow the money which it uses to invest in its projects. This may be a weighted average of the cost of the share capital and loan capital of a company. 

If money is borrowed, interest must be paid over the time period if money is loaned out, interest income is expected to accumulate. In other words, there is a time value associated with the money. Before money flows from different years can be combined, a compound interest factor must be employed to translate all of the flows to a common present time. The present is arbitrarily assumed often it is either the beginning of the venture or start of production. If future flows are translated backward toward the present, the discount factor is of the form (1 + i) , where i is the annual discount rate in decimal form (10% = 0.10) and n is the number of years involved in the translation. If past flows are translated in a forward direction, a factor of the same form is used, except that the exponent is positive. Discounting of the cash flows gives equivalent flows at a common time point and provides for the cost of capital. 

Table 9-3 gives examples of compound-interest factors and example compound-interest calculations. 

Annual Compound Interest It is more common to use compound interest, in which F and P are related by... 

Short-Interval Compound Interest If interest payments become due m times per year at compound interest, mn payments are required in n years. The nominal annual interest rate Y is divided by m to give the effective interest rate per period. Hence,... 

The annual interest rate equivalent to a compound-interest rate of 5 percent per month (i.e., i /m = 0.05) is calculated from Eq. (9-38) to be... 

Continuous Compound Interest As m approaches infinity, the time interval between payments becomes infinitesimally small, and in the hmit Eq. (9-37) reduces to... 

Numerically, the difference between continuous and annual compounding is small. In practice, it is probably far smaller than the errors in the estimated cash-flow data. Annual compound interest conforms more closely to current acceptable accounting practice. However, the small difference between continuous and annual compounding may be significant when apphed to very large sums of money. 

Compound Interest Factors 6% Compound Interest Factors ... 

Example 1 Capitalized Cost of Equipment Apiece of equipment has been installed at a cost of 100,000 and is expected to have a working life of 10 years with a scrap value of 20,000. Let us calculate the capitalized cost of the equipment based on an annual compound-interest rate of 5 percent. 

With a disbursement of 1000 in Year 0, the discounted breakeven point (DEEP) will be reached in 3 years at a compound-interest rate of 30 percent if the annual net profit Avp = 550.63 per year. Thus, a... 

It is even more difficult to think of profit as being a liability. Profit is the increase in money value available for distribution to the owners and effec tively represents the interest obtained on the capital. If the profit is not distributed, it represents an increase in capital by the normal concept of compound interest. Thus, if the individual s business makes a profit of 5000, the liabihty to the individual is increased to 15,000. With this concept in mind, Eq. (9-123) can be expanded to... 

A shortage of cash may prevent a company from taking advantage of large discounts available for bulk purchase of raw materials. The importance of the availability of adequate cash or near cash can be seen by considering an account payable within 28 days, with a 2 percent discount allowed if paid within 7 days. If cash is not available to pay the account within 7 days, this is then equivalent to paying 2 percent interest on the money for the remaining 21-day period, or an annual compound-interest rate of more than 41 percent. 

Aminonitrile formation on 125 with potassium cyanide and piperidine hydrochloride affords the derivative, 135. Hydrolysis as above gives the corresponding amide (136). Debenzylation is accomplished by catalytic reduction. Alkylation of the secondary amine with the side chain (96) used in the preparation of diphenoxylate affords pirintramide (138) This compound, interest-... 

This method, which is favored by many accountants today, takes into account the concept that money has a time value. This is because 2000 in 10 years time is not the same as 2000 now. Similarly, if a project earns 2000 in 10 years time this is not the same as 2000 spent now to help finance the project. If, instead of spending this 2000, it had been invested at compound interest, then in 10 years time it would have become a much larger... 

The selection of the discount factor depends on the financial policy of the business, but is usually 2-3 per cent above the current interest rates. Use of discounting methods will determine whether the project cost will produce a better return than by simply investing the capital involved at the highest compound interest rate or, if the capital cost has to be borrowed, whether the rate of return is much higher than the cost of borrowing. 

Investment.—We give an interesting illustration of a combined optimization and probability problem given by B. Boy. It is a trivial matter to show that an amount of money (1 + r) k, invested at the compound interest of r% over a period of h years will become a unit amount. 

In this case addition occurs fairly effectively to give the adduct in 88 % yield, and formation of telomers was not observed. The presence of the mobile bromine atom at the tertiary carbon atom makes these compounds interesting and promising synthons for further chemical transformations. 

The money earned in any year can be put to work (reinvested) as soon as it is available and start to earn a return. So money earned in the early years of the project is more valuable than that earned in later years. This time value of money can be allowed for by using a variation of the familiar compound interest formula. The net cash flow in each year of the project is brought to its present worth at the start of the project by discounting it at some chosen compound interest rate. 

A transmission tax is similar to a sales tax. It is levied whenever there is a transfer of funds. If an outside contractor hired an electrical subcontractor who in turn paid an electrician to perform a job, there would be three transmission taxes paid. One would be incurred when the corporation for whom the job was being performed paid the contractor. Another would occur when the contractor paid the subcontractor. The third would occur because the subcontractor paid the electrician. If the transmission tax were 7%, then the total transmission tax would be over 21%. (See the section on compound interest in Chapter 10.)... 

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. ... 

In the life insurance annuity a person contributes equal amounts over a number of years, and then at a given age (assuming he has not died previously) he receives a lump sum of money or some other form of payment. To determine how this compares with other forms of investment, the investor must determine at what interest rate his money would need to be invested in order to earn that lump sum in the same period of time. The first payment would earn compound interest for n periods. The second payment, which is made at the end of the first period, would earn interest for (n - 1) periods. The general rule is that each payment earns interest for one less period than the proceeding one. This can be expressed as... 

In general, one or more of three methods are used to justify major expenditures. The first, payback, is a measure of the time it will take for cumulative benefits to equal cumulative costs (time to break even). This, by itself, may not be sufficient to compare alternative investments and projects competing for the same limited resources so one of two other methods may be used. These methods, Net Present Value and Internal Rate of Return, consider the earning power of money in making comparisons. Because investments earn compound interest, a dollar to be gained in the future has less present value than one gained today. The NPV is computed by estimating the yearly... 

The thienothienopyridines are a relatively little-known class of compound. Interest in these systems arose through the possibility that they occurred in coal-derived products and their extended 7i-systems initiated interest for their interesting optical properties. Additionally, several differently substituted examples have antitumor activity <2002CPB656>, and may serve as DNA intercalating agents <2005MOL279>. 

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