Page 260 - Analysis, Synthesis and Design of Chemical Processes, Third Edition

9.2.1 Simple Interest

In simple interest calculations, the amount of interest paid is based solely on the initial investment.
Interest paid in any year = Pi s
For an investment period of n years, the total interest paid = Pi n
s
Total value of investment in n years = F = P + Pi n
s
n
(9.4)

If, instead of setting the earned interest aside, it were reinvested, the total amount of interest earned would
be greater. When earned interest is reinvested, the interest is referred to as compound interest.

9.2.2 Compound Interest

Let us determine the future value of an investment, F , after n years at an interest rate of i per year for an
n
initial investment of P when the interest earned is reinvested each year.
a. At the start, we have our initial investment = P.
b. In year 1, we earn Pi in interest.
For year 2, we invest P + Pi or P(1 + i).
c. In year 2, we earn P(1 + i)i in interest.
2
For year 3, we invest P(1 + i)+ P(1 + i)i, or P(1 + i) .
2
d. In year 3, we earn P(1 + i) i in interest.
2
2
3
For year 4, we invest P(1 + i) + P(1 + i) i, or P(1 + i) .
n
e. By induction we find that after n years the value of our investment is P(1 + i) .
Thus, for compound interest we can write
(9.5)

We can reverse the process and ask, How much would I have to invest now, P, in order to receive a
certain sum, F , in n years’ time? The solution to this problem is found by rearranging Equation (9.5):
n

(9.6)