CH6 Process Engineering Economics - James R. Couper

# CH6 Process Engineering Economics - James R. Couper - 6...

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6 Time Value of Money When a person loans money, a charge is made for the use of these borrowed funds. The lender perhaps could have invested the funds somewhere else and made a proﬁt; therefore, the interest is the compensation for the foregone proﬁt. The borrower may look upon this interest as the cost of renting money. The amount charged depends on the scarcity of money, the size of the loan, the length of the loan, the risk the lender feels that the loan may not be paid back, and the prevailing economic conditions. Because engineers may be involved in the presentation and/or the evaluation of an investment of money in a venture, it is important that they understand the time value of money and how it is applied in the evaluation of projects. Later we shall see that in modern times, the term “return on investment” is used for the classical term “interest.” It is the charge paid for borrowed money. 6.1 INTEREST RATE The interest rate is the ratio of the interest charged at the end of a period (usually 1 year) to the amount of money owed at the beginning of the period expressed as a percentage. For example, if \$10 of interest is payable at the end of a year on a loan of \$100, the interest rate is \$10/\$100 or 0.10 or 10% interest. When an interest rate is quoted, it is usually expressed on an annual basis unless otherwise quoted. The nominal interest is 10% without any consideration of the effect of compounding during the year. Interest may be compounded on bases other than annual and this topic will be considered later in this chapter [1].

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6.2 INTEREST NOMENCLATURE The nomenclature used in interest calculations may be found in Table 6.1. The terminology presented in the table is to acquaint the reader with the numerous meanings for the same symbols and will be used throughout the text. 6.3 SIMPLE INTEREST If P is the principal, the loan amount or the original capital, n is the number of interest periods, and i is then interest rate for the period, the amount of simple interest I earned for n periods is I ¼ Pin ð 6 : 1 Þ Ultimately, the principal must be paid plus the simple interest for n periods at a future time, F ; therefore, F ¼ P þ I ¼ P þ Pin ¼ P ð 1 þ in Þð 6 : 2 Þ The interest is charged on the original loan and not on the unpaid balance. Simple interest is paid at the end of each time interval. Although the simple interest concept still exists, it is seldom used [1]. Example 6.1 If \$1000 has been borrowed at 10% simple interest for 4 years, develop a table of values for the interest owed each year and the total amount owed. Table 6.2 is the solution of the simple interest calculation in Example 6.1. T ABLE 6.1 Interest Nomenclature Symbol Deﬁnition F Future sum Future value Future worth Future amount P Principal Present worth Present value Present amount A End of period payment in a uniform series
6.4 COMPOUND INTEREST Since interest has a time value, often the lender will invest this interest and earn more additional interest [1]. It is assumed that the interest is not withdrawn but is

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CH6 Process Engineering Economics - James R. Couper - 6...

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