Page 250 - Plant design and economics for chemical engineers

220 PLANT DESIGN AND ECONOMICS FOR CHEMICAL ENGINEERS

Amount with continuous compound interest

Amount with discrete compound interest

FIGURE 7-1
Comparison among total
amounts accumulated with sim-
ple interest, discrete compound
interest, and continuous com-
Time in years pound nominal interest.

and the interest is compounded at half-year periods. A rate of this type would
be referred to as “6 percent compounded semiannually.” Interest rates stated in
this form are known as nominal interest rates. The actual annual return on the
principal would not be exactly 6 percent but would be somewhat larger because
of the compounding effect at the end of the semiannual period.
It is desirable to express the exact interest rate based on the original
principal and the convenient time unit of 1 year. A rate of this type is known as
the effective interest rate. In common engineering practice, it is usually preferable
to deal with effective interest rates rather than with nominal interest rates. The
only time that nominal and effective interest rates are equal is when the interest
is compounded annually.
Nominal interest rates should always include a qualifying statement indi-
cating the compounding period. For example, using the common annual basis,
$100 invested at a nominal interest rate of 20 percent compounded annually
would amount to $120.00 after 1 year; if compounded semiannually, the amount
would be $121.00; and, if compounded continuously, the amount would be
$122.14. The corresponding effective interest rates are 20.00 percent, 21.00
percent, and 22.14 percent, respectively.
If nominal interest rates are quoted, it is possible to determine the
effective interest rate by proceeding from Eq. (5).
s = P(1 + i)”

In this equation, S represents the total amount of principal plus interest due
after n periods at the periodic interest rate i. Let r be the nominal interest rate
under conditions where there are m conversions or interest periods per year.