Page 69 - CalcBus_Flipbook

CH 8] Calculating Business 8-11

The problem can also be solved by using two different compound interest factors as long
as the sum of the n values = 60. Look at n values 40 and 20 as 40 + 20 = 60.

(b) 40 + 20 = 60 n rows
1.48886373 x 1.22019004 = 1.81669669 amount for CF
Factor x investment = amount in fund
1.81669669 x $4,000 = $7,266.79 Compound value in fund

Though the calculated compound interest factors for (a) and (b) are not absolutely equal for the
n rows used at 1% column, the end result is equal.

(a) (b)
1.81669670 ≈ 1.81669669
$7,266.79 = $7,266.79

In the above discussion the last digit on the right varies slightly because these amounts and
those in the table have been rounded to the eighth place. With a twelve-digit calculator the
differences are greater, but these variations are insignificant when the principal is relatively
small.

Daily Compounding of Interest
Computer software with compounding algorithms have enabled banks to more aggressively
compete for customers, both depositors and borrowers, by offering daily compounding on
interest. If a depositor is encouraged to do business with the bank and the customer services
are such that they like the business atmosphere, then that depositor will seek loans based on
their relationship with the bank.
Most banks pay interest monthly, but the compounding interval can vary. Currently Bank
of America and Wells Fargo Bank do offer continuous compounded interest, interest calculated
daily. Chase on the other hand compounds and pays monthly. The best way to determine how
often your savings interest is calculated is to ask the bank you do business with. Why do banks
offer a variety of interest plans? It is called Capitalism; banks compete for customers and in
their offerings of savings, credit cards, and loans for whatever their customers need, banks are
willing to devise structures that will compete effectively for customers.
Tables of factors have been prepared at various interest rates for both daily compounding
and continuous compounding. Of course, the compound interest equation may be used.
When the number of conversion periods (n) is large, factoring the exponent and using
constant multiplication may be combined to reduce the number of times the = key is pressed.
First consider the relatively small exponent of 6.

6
Example A: Calculate: 1.08 . Read as “one point zero eight to the 6 power. The 6 th
th
power is also called an exponent.
6
Solution algorithm: (a) 1.08 = 1.08 x 1.08 x 1.08 x 1.08 x 1.08 x 1.08
6
(b) 1.08 = (1.08 x 1.08)(1.08 x 1.08)(1.08 x 1.08)
6
2
2
2
(c) 1.08 = 1.08 x 1.08 x 1.08
6
2 3
(d) 1.08 = (1.08 )
6
(e) 1.08 = 1.08 2x3
2x3
6
In this Solution algorithm at line (e), 1.08 = 1.08 2x3 , the expression 1.08 may be

interpreted to mean square 1.08, (1.08 x 1.08), and then raise the result of the squaring to the 8
power of 3, (1.08 x 1.08 x 1.08). Recall that when a number is being raised to a power, n, with a
hand calculator, the = key is pressed n — 1 times. The first step in this procedure, however, is
to break down the exponent into two or more factors as illustrated above then with your hand
calculator the key strokes would be:
CL 1.08 X = X = = 1.586874

power 2 power 3 Exponent ( 2 x 3 = 6 )
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