### Engineering Economics - Terminology and Symbols

Sample units are indicated.

P = value or amount of money at a time designated as the present or time 0. Also P is referred to as present worth (PW), present value (PV), net present value (NPV), discounted cash ﬂ ow (DCF), and capitalized cost (CC); monetary units, such as dollars

F = value or amount of money at some future time. Also F is called future worth (FW) and future value (FV); dollars

A = series of consecutive, equal, end-of-period amounts of money. Also A is called the annual worth (AW) and equivalent uniform annual worth (EUAW); dollars per year, euros per month

n = number of interest periods; years, months, days

i = interest rate per time period; percent per year, percent per month

t = time, stated in periods; years, months, days

The symbols P and F represent one-time occurrences: A occurs with the same value in each inter- est period for a speciﬁ ed number of periods. It should be clear that a present value P represents a single sum of money at some time prior to a future value F or prior to the ﬁ rst occurrence of an equivalent series amount A .

It is important to note that the symbol A always represents a uniform amount (i.e., the same

amount each period) that extends through consecutive interest periods. Both conditions must exist before the series can be represented by A .

The interest rate i is expressed in percent per interest period, for example, 12% per year. Un- less stated otherwise, assume that the rate applies throughout the entire n years or interest periods. The decimal equivalent for i is always used in formulas and equations in engineering econ- omy computations.

All engineering economy problems involve the element of time expressed as n and interest rate i . In general, every problem will involve at least four of the symbols P , F , A , n , and i , with at least three of them estimated or known.

Additional symbols used in engineering economy are deﬁ ned in Appendix E

**EXAMPLE 1.6**

Today, Julie borrowed $5000 to purchase furniture for her new house. She can repay the loan in either of the two ways described below. Determine the engineering economy symbols and their value for each option.

**(a)**Five equal annual installments with interest based on 5% per year.

**(b)**One payment 3 years from now with interest based on 7% per year.

**Solution**

**(a)**The repayment schedule requires an equivalent annual amount A , which is unknown.

P = $5000 i =5% per year n = 5 years A = ?

**(b)**Repayment requires a single future amount F, which is unknown.

P = $5000 i = 7% per year n = 3 years F = ?

**EXAMPLE 1.7**

You plan to make a lump-sum deposit of $5000 now into an investment account that pays 6% per year, and you plan to withdraw an equal end-of-year amount of $1000 for 5 years, starting next year. At the end of the sixth year, you plan to close your account by withdrawing the re- maining money. Deﬁ ne the engineering economy symbols involved.

**Solution**

All five symbols are present, but the future value in year 6 is the unknown.

P = $5000

A = $1000 per year for 5 years

F = ? at end of year 6

i = 6% per year

n = 5 years for the A series and 6 for the F value

**EXAMPLE 1.8**

Last year Jane’s grandmother offered to put enough money into a savings account to generate $5000 in interest this year to help pay Jane’s expenses at college. (a) Identify the symbols, and (b) calculate the amount that had to be deposited exactly 1 year ago to earn $5000 in interest now, if the rate of return is 6% per year.

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