Page 256 - Plant design and economics for chemical engineers

226 PLANT DESIGN AND ECONOMICS FOR CHEMICAL ENGINEERS

future amount is the present pr’ cipal which must be deposited at a given
interest rate to yield the desired am nt at some future date.?
In Eq. (5), S represents the amou interest periods if the
‘% t available after n
initial principal is P and the discrete compound-interest rate is i. Therefore, the
present worth can be determined by merely rearranging Eq. (5).
1
Present worth = P = S 07)
(1 + i)”
The factor l/(l + i>” is commonly referred to as the discrete single-payment
present-worth factor.
Similarly, for the case of continuous interest compounding, Eq. (12) gives

Present worth = P = SA (18)
e
Some types of capital are in the form of bonds having an indicated value at
a future date. In business terminology, the difference between the indicated
future value and the present worth (or present value) is known as the discount.
Example 4 Determination of present worth and discount. A bond has a maturity
value of $1000 and is paying discrete compound interest at an effective annual rate
of 3 percent. Determine the following at a time four years before the bond reaches
maturity value:
(a) Present worth.
(b) Discount.
(c) Discrete compound rate of effective interest which will be received by a
purchaser if the bond were obtained for $700.
(d) Repeat part (a) for the case where the nominal bond interest is 3 percent
compounded continuously.
solution
(a) By Eq. (171, present worth = S/(l + i)” = $lOOO/(l + 0.03j4 = $888
(b) Discount = future value - present worth = $looO - $888 = $112
(c) Principal = $700 = S/(l + i)” = $lOOO/(l f ij4

1000 1’4
- 1 = 0.0935 or 9.35%
700
I= (-1
.
(d) By Eq. (18), present worth = S/e’” = $1000/e(0.03X4) = $869
ANNUITIES
An annuity is a series of equal payments occurring at equal time intervals.
Payments of this type can be used to pay off a debt, accumulate a desired

tin the analyses presented in this chapter, effects of inflation or deflation on future worth are not
considered. See Chap. 11 (Optimum Design and Design Strategy) for information on the strategy for
dealing with inflation or deflation in design economic evaluations.