Page 70 - CalcBus_Flipbook

8-12 Compound Interest CH 8]

There are times using a hand calculator with an exponent of a large number such as 20, the
number of times we strike the = key can cause confusion; that is we lose count as to how many
times we have struck the = key. Is it obvious that you need to be careful and count each = key
strike? In any case, it is a good idea to break this exponent number into separate actions of
smaller counts to maintain your accuracy with the results.

Example B: Calculate: 1.08 20

20
Solution algorithm: 1.08 = 1.08 2x10
20
1.08 = 1.08 2x2x5 your = key strikes will be n-1

With your hand calculator the key strokes are:
CL 1.08 X = X = X = = = = 4.6609571

power 2 power 2 power 5

Exponent Power 2 2 5
= key strikes (n-1 =) (2-1=) 1 (2-1=) 1 (5-1=) 4

Let’s return to our discussion on the compound interest equation where:

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

Over one year, we know that T (Time) has a value of 1 and any number multiplied by 1
equals that number.
For daily compounding, the i value is for the Interest rate per period in decimal form; In our
equation the i value will need to be altered to r/365 (or 366 for a leap year) unless the problem
specifies a 360-day year. The r value is the interest rate as a decimal, such that given as 6%
interest, it is written as 0.06 and on your calculator you would press the “.” key then the 0 key
followed by the 6 key.

The equation becomes:
n
S P = P (1 + r/365 )
These are the steps to follow to determine the compound amount:
1. Factor the exponent n completely.
2. Calculate the value of r/365 where r is a decimal value for the interest rate.
3. Add 1 to the value of r/365.
4. Raise (1 + r/365) to the power of n by using the factors.
5. Multiply the result by the principal.
6. Remember that the T value is 1 for 1 year, and 1 times any number equals the number
thus:
n
n
S P = P (1 + r/365 ) x T (where T =1) becomes S P = P (1 + r/365 )

Example C: Declan Branson deposited $3,000 in an account that pays 6% interest
compounded daily. Calculate (a) the compound amount and (b) the compound
interest at the end of 30 days.

Solution algorithm: S P = P (1 + r/365) n
S P = P (1 + 0.06/365) n
P = $3,000
r = 6% = 0.06
30
n = 30 S P = 3,000 x (1 + 0.06/365)

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