Page 66 - CalcBus_Flipbook

8-4 Compound Interest CH 8]

Example A: Lynn Redgrave deposited $1,500 in a fund that pays 8% interest
compounded annually. Calculate (a) the amount in the fund and (b) the
compound interest at the end of 3 years.

Solution: (a) Original principal ................................................................. $1,500.00
Interest for first year ($1,500 x 0.08 x 1yr =) .............................. 120.00
Principal for second year ........................................................... $1,620.00
Interest for second year ($1,620 x 0.08 x 1yr =) ......................... 129.60
Principal for third year .............................................................. $1,749.60
Interest for third year ($1,749.60 x 0.08 x 1yr=) ........................ 139.97
Amount in fund at the end of 3 years ........................................ $1,889.57

(b) $1,889.57 — $1,500.00 = $389.57 compound interest

The algorithm is summarized in the following compound-interest equation:

S = Sum of principal and interest—compound amount
P = Principal
n
S = P x (1 + i) x T i = Interest rate per period in decimal form
n = Total number of interest periods
T = Time

Substituting the appropriate numbers from Example A in the equation yields:

3
S = $1,500 x (1 + 0.08) x 1/year = $1,889.57
Order of
Operations: ODER OF OPERATIONS
PEMDAS Now comes the time when a small discussion on the “order of operations” is in order for
a complete understanding of the mathematics; especially for Calculating Business. In
1. Parentheses. mathematics there exists a rigid order in which equations are to be solved, and thus it is
2. Exponents and important that know, understand and apply this order before this discussion can proceed
Roots √ further. The order of operations defines what is done first, second and third and so forth to
3. Multiplication and solve an equation. The Order of Operation is:
Division (from left  Parentheses. ( ), { }, and [ ]
to right)  Exponents and roots. X X n , or X –n , and √
3
,
4. Addition and  Multiplication and Division (from left to right) *, , and /, or ÷
Subtraction (from
left to right)  Addition and Subtraction (from left to right) +, and —

and may be abbreviated as PEMDAS:

Exponent: a quantity Mathematics requires a rigid order in which equations are to be resolved, and thus
representing the power equations such as previously stated must be written to conform to this rigid order. Such
to which a given 3

number or expression that S for 3 years = 1,500 x (1 + 0.08) x 1/year may be stated and solved as:
is to be raised, usually 3
expressed as a raised (1 + 0.08) x 1/year x $1,500 = S for 3 years
symbol beside the
number or expression Same qualities and values as the first equation except this one conforms to the rigid
3
(e.g. 3 in 2 = 2 × 2 × order of PEMDAS. This mathematical statement, equation, though written differently than
2). the one above actually, is the more correct form and will conform to your hand calculator.
Understand that though you have solved this problem mechanically, as demonstrated
above, following the rigid order allows you to make the same calculation with your hand
calculator with greater facility (easier).

How will PEMDAS work with our current equation?

3
(1 + 0.08) x 1/year x $1,500 = S for 3 years

First you can see that the rigid order begins with Parentheses and the first statement
3
in our equation is a Parenthesis (1 + 0.08) with an exponent value of 3. Earlier this was
defined as n but we know that n refers to the total number of interest periods and in our
problem that is 3; interest payments each year for a total of 3 years. Thus n = 3, as an
exponent. Still the numbers in the parenthesis must be dealt with first. What we have is 1
+ 0.08. Performing the arithmetic indicated and you arrive at a value of (1 + 0.08 =) 1.08.

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