Page 255 - Plant design and economics for chemical engineers

INTEREST AND INVESTMENT COSTS 225

Example 3 Use of digital computer to give tabulated values of amount accumula-
ted with continuous interest compounding. Present the digital computer program
and the tabulated prin ut to six significant figures giving the amount to which an
initial principal of $100 ill accumulate year by year from 1 to 20 years with
“%
continuous interest compounding based on a nominal interest rate of 20 percent.
Solution. The equation to be solved on the digital computer is
S = Per”
where S will be evaluated to six significant figures for
n = 1,2,3 ,..., 20
P=$loo
1 = 0.20
The Fortran IV program and the computer print-out follow:
$IBJOB MAP
$IBFTC DECK 1
DOlN= 1,20
A N = N
S = lOO.*EXP(.2O*AN)
1 WRITE(6,2)N, S
2 FORMAT(I4,F12.3)
END
$ENTRY

Printout
1 122.140 11 902.501
2 149.182 12 1102.318
3 182.212 13 1346.374
4 222.554 14 1644.465
5 271.828 15 2008.554
6 332.012 16 2453.253
7 405.520 17 2996.410
8 495.303 18 3659.823
9 604.965 19 4470.118
10 738.906 20 5459.815

(NOTE: The preceding illustrates the method used to prepare tabulated results of
factors and emphasizes the simplicity of the procedure with a digital computer. This set
of results represents a standard exponential function available in tabulated form in
standard mathematical tables. See Prob. 8 at the end of this chapter for a requested
computer solution for a more complicated continuous-interest case.)

PRESENT WORTH AND DISCOUNT
It is often necessary to determine the amount of money which must be available
at the present time in order to have a certain amount accumulated at some
definite time in the future. Because the element of time is involved, interest
must be taken into consideration. The present worth (or present value) of a