Answer
For $500 with compound interest at 5% per annum calculated every 6 months.
Amount invested ($)
|
period
|
Interest Rate |
Interest for 6 months($)
|
New balance ($)
|
500
|
1
|
5
|
12.50
|
512.50
|
512.50
|
2
|
5
|
12.81
|
525.31
|
525.31
|
3
|
5
|
13.13
|
538.44
|
538.44
|
4
|
5
|
13.46
|
551.9
|
551.90
|
5
|
5
|
13.80
|
565.70
|
565.70
|
6
|
5
|
14.14
|
579.84
|
The percentage increase for the three year period with interest compounded every six months is [(579.84 − 500)/500] × 100 = 15.968%
For $500 with compound interest at 5% per annum calculated every 3 months.
Repeating the above table for 12 periods (every 3 months) gives a final amount of $580.38 which is a percentage increase of 16.08%
For $500 with compound interest at 5% per annum calculated every 1 month. Using the formaula for compound interest:
where P = $500, r = 5/12% per month and n = 36
gives a final amount of $580.74 which is a percentage increase of 16.15%
It would appear that as the time period for calculating compound interest is decreased, the amount of interest gained is increased.