Series payment

The following expressions can be used to determine the NPW for single or uniform series payments over a time period, n ... 

Table 17.7 Time Value of Money Annuity Factors—Uniform-Series Payments—Compound Interest (Details Presented in Section 17.5) ...

In this section, we will first formulate the relationship between a present lump sum, P, and future uniform series payments. A, and then from that relationship we will develop the formula that relates the uniftirm series payments A to a future lump sum P. This approach is much easier to follow as you will see. lb derive these relationships, let us first consider a situation where we have borrowed some money, denoted by P, at am annuad interest rate i from a bank, amd we are planning to pay the loan yearly, in equal amounts A, in years, as shown in Figure 20.4. 

It is important to note that Equations (20.9), (20.10), (20.12), and (20.13) apply to a situation wherein the uniform series of payments or revenues occur annually. Well, the next question is, how do we handle situations where the payments are made monthly For example, a car or a house loan payments occur monthly. Let us now modify our findings by considering the relationship between present value P and uniform series payments or revenue A that occur more than once a year at the same frequency as the fiequency of compounding interest per year. 

A = uniform series payment, or uniform series revenue ( ) i = nominal interest rate = effective interest rate ti = number of years... 

Take the capital cost and spread it as a series of equal annual payments A made at the end of each year over n years. The first payment gains interest over (n — 1) years, and its future value after (n - 1) years is... 

A fourth method of computing depreciation (now seldom used) is the sinking-fund method. In this method, the annual depreciation A is the same for each year of the life of the equipment or plant. The series of equal amounts of depreciation Aq, invested at a fractional interest rate i and made at the end of each year over the life of the equipment or plant of s years, is used to build up a future sum of money equal to (Cpc S). This last is the fixed-capital cost of the equipment or plant minus its salvage or scrap value and is the total amount of depreciation during its useful life. The equation relating i Fc S) and Ao is simply the annual cost or payment equation, written either as... 

Single payment Uniform annual series Single payment Uniform annual series ... 

Annual Cost or Payment A series of equal annual payments A invested at a fractional interest rate i at the end of each year over a period of n years may be used to build up a future sum of money E These relations are given bv... 

Equation (9-41) represents the future sum of a series of uniform annual payments that are invested at a stated interest rate over a period of years. This procedure defines an ordinaiy annuity. Other Forms of annuities include the annuity due, in which payments are made at the beginning of the year instead of at the end and the deferred annuity, in which the first payment is deferred for a definite number of years. 

An annuity is a series of equal periodic payments that last for a given length of time. This is the usual way an individual pays for the capital necessary to purchase a new home, or buys life insurance. 

Present value of a series of uniform future payments each of value 1 starting in period m and ending with period tv. 

Future value of a series of (not necessarily equal) payments Pk ... 

The future worth S of a series of n uniform payments each of amount P is... 

The NVLAP is comprised of a series of laboratory accreditation programs (LAPs), depending on what is requested and what is needed. Each LAP includes specific calibration and/or test standards and related methods and protocols assembled to satisfy the unique needs for accreditation in a field of testing or calibration. NVLAP accredits public and private laboratories based on evaluation of their technical qualifications and competence to carry out specific calibrations or tests. All are based on the ISO/IEC Guide 25 discussed in Section 2. The process involves an application and the payment of fees. This is followed by an on-site assessment. If deficiencies are found, these must be resolved to the satisfaction of the assessment team. The laboratory then participates in proficiency testing (Section 5.7) and a technical evaluation. 

U.S. multinational firms to a series of multilateral reforms of intellectual property rights regimes undertaken by 12 countries over the 1982-1999 period. They found that intellectual property rights regime changes result in increases in royalty payment flows to parent firms, and that some of the increased royalty flows represents the transfer of new technologies to the host country. 

Early Withdrawal Penalty. There is a 10-percent penalty for taking money out of your tax-deferred retirement accounts before age 59-1/2. But there are two exceptions. One is if you retire at age 55 or later, are disabled, or die. The other is if you receive your money in a series of substantially equal periodic payments. If you choose this route, you must stay with the program at least five years or until you reach age 59-1/2. 

An annuity is a series of equal payments occurring at equal time intervals. Payments of this type can be used to pay off a debt, accumulate a desired... 

In essence, the CRC converts the TCI (a one-time cost) to a series of equal annual payments over the fife of the project. 

The casein content of milk is an important indicator of cheese yield, and cheese yield formulas are used to determine milk payment in some cheese plants. Milks of similar protein content but dissimilar casein/whey ratio do not produce the same cheese yield. The methods presently used for casein estimation are based on precipitation of casein from the milk and involve a series of steps including centrifugation, aspiration of fat, filtration, drying and weighing. Two methods for the determination of the casein content of milk with the use of a commercial IR milk analyser have been described [24,... 

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