### Engineering Economics

ENGINEERING ECONOMICS

Engineers, managers, purchasing agents, and others are often required to plan and evaluate project alternatives, and make economic decisions that may greatly affect the success or failure of a project. The goals of a project, such as reducing manufacturing cost or increasing production, selection of machine tool alternatives, or reduction of tooling, labor and other costs, determine which of the available alternatives may bring the most attractive economic return. Various cost analysis techniques that may be used to obtain the desired outcome are discussed in the material that follows.

Interest

Interest is money paid for the use of money lent for a certain time. Simple interest is the interest paid on the principal (money lent) only. When simple interest that is due is not paid, and its amount is added to the interest-bearing principal, the interest calculated on this new principal is called compound interest. The compounding of the interest into the principal may take place yearly or more often, according to circumstances.

Interest Formulas.—The symbols used in the formulas to calculate various types of interest are:

P =principal or amount of money lent
I =nominal annual interest rate stated as a percentage, i.e., 10 per cent per annum
Ie =effective annual interest rate when interest is compounded more often than once a year (see Nominal vs. Effective Interest Rates)
i =nominal annual interest rate per cent expressed as a decimal, i.e., if
I = 12 per cent, then i = 12⁄100 = 0.12
n =number of annual interest periods
m =number of interest compounding periods in one year
F =a sum of money at the end of n interest periods from the present date that is equivalent to P with added interest i
A =the payment at the end of each period in a uniform series of payments continuing for n periods, the entire series equivalent to P at interest rate i

Note: The exact amount of interest for one day is 1⁄365 of the interest for one year. Banks, however, customarily take the year as composed of 12 months of 30 days, making a total of 360 days to a year. This method is also used for home-mortgage-type payments, so that the interest rate per month is 30⁄360 = 1⁄12 of the annual interest rate. For example, if I is a 12 per cent per annum nominal interest rate, then for a 30-day period, the interest rate is (12 × 1⁄12) = 1.0 per cent per month. The decimal rate per month is then 1.0⁄100 = 0.01.

Simple Interest.—The formulas for simple interest are:

Interest for n years = P x i x n
Total amount after n years, S = P + P x i x n

Example:For \$250 that has been lent for three years at 6 per cent simple interest: P = 250; I = 6; i = I/100 = 0.06; n = 3.

F = 250 250 0.06 + 250 45 ( ) × × 3 + \$295

Compound Interest.—The following formulas apply when compound interest is to be computed and assuming that the interest is compounded annually.