To Calculate Compound Interest:
Meaning of Words
Interest:
Is the money you pay to
the bank when borrowing money from them. It can also be the money the
bank pays you for keeping your money. It is calculated by multiplying the rate by the balance.
Rate:
A percentage (e.g. 4%, 9.6%, 11%) used to calculate interest.
Balance:
The amount of money a person has in a bank account. It is usually called
the "Principal".
Compound Interest:
Interest calculations made during a given period when money
earns interest on top of the original calculated balances during that period at given intervals. (e.g. look
at the example below)
To calculate compound interest annually:
The annual interest is divided by the given intervals, then the
first interval and every successive interval is multiplied by that rate and
added to the new balance at every interval. (See the example below)
Example...
A person borrows $320
at 13.5% p.a. compounded monthly for 1 year. What will be the balance after 12 months?
13.5%
÷ 12 months = 1.125%, which is the rate for 1 month.
Principal for 1st month 
= 
$320 
Original Balance = $320.00 
Interest for 1st month 
= 
1.125%
of $320 
$320.00
×1.125% = $3.60 

= 
$3.60 

Principal for 2nd month 
= 
$323.60 
$320.00 + $3.60 = $323.60 
Interest for 2nd month 
= 
1.125% of $323.60 
$323.60
×1.125% = $3.64 

= 
$3.64 

Principal for 3rd month 
= 
$327.24 
$323.60 + $3.64 = $327.24 
Interest for 3rd month 
= 
1.125% of $327.24 
$327.24×1.125% = $3.68 

= 
$3.68 

Principal for 4th month 
= 
$330.92 
$327.24 + $3.68 = $330.92 
Interest for 4th month 
= 
1.125% of $330.92 
$330.92
×1.125% = $3.72 

= 
$3.72 

Principal for 5th month 
= 
$334.64 
$330.92 + $3.72 = $334.64 
Interest for 5th month 
= 
1.125% of $334.64 
$334.64
×1.125% = $3.76 

= 
$3.76 

Principal for 6th month 
= 
$338.40 
$334.64 + $3.76 = $338.40 
Interest for 6th month 
= 
1.125% of $338.40 
$338.40
×1.125% = $3.81 

= 
$3.81 

Principal for 7th month 
= 
$342.21 
$338.40 + $3.81 = $342.21 
Interest for 7th month 
= 
1.125% of $342.21 
$342.21
×1.125% = $3.85 

= 
$3.85 

Principal for 8th month 
= 
$346.06 
$342.21 + $3.85 = $346.06 
Interest for 8th month 
= 
1.125% of $346.06 
$346.06
×1.125% = $3.89 

= 
$3.89 

Principal for 9th month 
= 
$349.95 
$346.06 + $3.89 = $349.95 
Interest for 9th month 
= 
1.125% of $349.95 
$349.95
×1.125% = $3.94 

= 
$3.94 

Principal for 10th month 
= 
$353.89 
$349.95 + $3.94 = $353.89 
Interest for 10th month 
= 
1.125% of $353.89 
$353.89
×1.125% = $3.98 

= 
$3.98 

Principal for 11th month 
= 
$357.87 
$353.89 + $3.98 = $357.87 
Interest for 11th month 
= 
1.125% of $357.87 
$357.87
×1.125% = $4.03 

= 
$4.03 

Principal for 12th month 
= 
$361.90 
$357.87 + $4.03 = $361.90 
Quick Way:
320 × (1 + 0.01125)^{11} = $361.90
Principal = $320
Rate =
1.125% or 0.01125
(1.125/100) interest charged each month.
Number of months times the rate is to be squared:
11 times (12 months  1), because the first month has already been calculated.
Formula:
C = P ×
(1 + R)^{n  1}
