Page 274 - Analysis, Synthesis and Design of Chemical Processes, Third Edition

Example 9.16

I invest money in a savings account that pays a nominal interest rate of 6% p.a. compounded monthly. I
open the account with a deposit of $1000 and then deposit $50 at the end of each month for a period of
two years, followed by a monthly deposit of $100 for the following three years. What will the value of my
savings account be at the end of the five-year period?

First, draw a discrete CFD (Figure E9.16).

Figure E9.16 Cash Flow Diagram for Example 9.16

Although this CFD looks rather complicated, it can be broken down into three easy sub-problems:
1. The initial investment
2. The 24 monthly investments of $50

3. The 36 monthly investments of $100

Each of these investments is brought forward to the end of month 60.

F = ($1000)(F/P, 0.005, 60) + ($50)(F/A, 0.005, 24)(F/P, 0.005, 36) + ($100)(F/A, 0.005, 36)

Note: The effective monthly interest rate is 0.06/12 = 0.005.

There are many ways to solve most complex problems. No one method is more or less correct than
another. For example, the discrete CFD could be considered to be made up of a single investment of
$1000 at the start, a $50 monthly annuity for the next 60 months, and another $50 annuity for the last 36
months. Evaluating the future worth of the investment gives

F = ($1000)(F/P, 0.005, 60) + ($50)(F/A, 0.005, 60) + ($50)(F/A, 0.005, 36)