Page 246 - Plant design and economics for chemical engineers

INTEREST AND INVFiSTMENT COSTS 217

giving someone the use of $1000 for a period of one year, the principal would be
$1000, and the rate of interest would be lOO/lOOO = 0.1 or 10 percent/year.
The simplest form of interest requires compensation payment at a con-
stant interest rate based only on the original principal. Thus, if $1000 were
loaned for a total time of 4 years at a constant interest rate of 10 percent/year,
the simple interest earned would be
$1000 x 0.1 x 4 = $400
If P represents the principal, n the number of time units or interest
periods, and i the interest rate based on the length of one interest period, the
amount of simple interest Z during n interest periods is
Z=Pin (1)
The principal must be repaid eventually; therefore, the entire amount S of
principal plus simple interest due after n interest periods is
S = P + Z = P(l + in) (2)

Ordinary and Exact Simple Interest
The time unit used to determine the number of interest periods is usually
1 year, and the interest rate is expressed on a yearly basis. When an interest
period of less than 1 year is involved, the ordinary way to determine simple
interest is to assume the year consists of twelve 30-day months, or 360 days. The
exact method accounts for the fact that there are 365 days in a normal year.
Thus, if the interest rate is expressed on the regular yearly basis and d
represents the number of days in an interest period, the following relationships
apply:

Ordinary simple interest = ZV&

d
Exact simple interest = pi= (4)

Ordinary interest is commonly accepted in business practices unless there
is a particular reason to use the exact value.

Compound Interest
In the payment of simple interest, it makes no difference whether the interest is
paid at the end of each time unit or after any number of time units. The same
total amount of money is paid during a given length of time, no matter which
method is used. Under these conditions, there is no incentive to pay the interest
until the end of the total loan period.
Interest, like all negotiable capital, has a time value. If the interest were
paid at the end of each time unit, the receiver could put this money to use for
earning additional returns. Compound interest takes this factor into account by