Page 251 - Plant design and economics for chemical engineers

INTEREST AND INVESTMENT COSTS 221
Then the interest rate based on the length of one interest period is r/m, and
the amount S after 1 year is
m
\ S after 1 year (6)

Designating the effective interest rate as ieR, the amount S after 1 year
can be expressed in an alternate form as
S after 1 year = P(l + ieff) (7)
By equating Eqs. (6) and (71, the following equation can be obtained for
the effective interest rate in terms of the nominal interest rate and the number
of periods per year:
m
Effective annual interest rate = i,, = - 1 (8)
Similarly, by definition,

= r (9)

Example 1 Applications of different types of interest. It is desired to borrow
$1000 to meet a financial obligation. This money can be borrowed from a loan
agency at a monthly interest rate of 2 percent. Determine the following:
(a) The total amount of principal plus simple interest due after 2 years if no
intermediate payments are made.
(b) The total amount of principal plus compounded interest due after 2 years if no
intermediate payments are made.
(c) The nominal interest rate when the interest is compounded monthly.
(d) The effective interest rate when the interest is compounded monthly.
solwiotl
(a) Length of one interest period = 1 month
Number of interest periods in 2 years = 24
For simple interest, the total amount due after n periods at periodic interest
rate i is
S = P(l + in) (2)
P = initial principal = $1000
i = 0.02 on a monthly basis
n = 24 interest periods in 2 years
S = $lOOO(l + 0.02 x 24) = $1480
(b) For compound interest, the total amount due after n periods at periodic
interest rate i is
S = P(l + i)” (5)
s = $1000(1 + o.02)24 = $1608
(c) Nominal interest rate = 2 X 12 = 24% per year compounded monthly