Business Mathematics and Statistics · Ch 4 — Simple and Compound Interest
Difference Between Simple and Compound Interest
Difference Between Simple and Compound Interest
Both methods start from the same principal, rate and time, yet they behave very differently over more than one period. The table below sets out the distinction the Odisha CHSE Business Mathematics and Statistics syllabus expects a student to be able to state:
| Basis | Simple Interest | Compound Interest |
|---|---|---|
| Base for interest | Always the original principal | Principal plus interest accumulated so far |
| Interest each period | Same (constant) every period | Increases every successive period |
| Growth pattern | Linear (arithmetic) | Geometric (multiplicative) |
| Formula | ||
| First period | Equal to CI of the first period | Equal to SI of the first period |
| Amount for the same | Smaller (for ) | Larger (for ) |
The first period is always equal. Because compounding has not yet had a chance to act, the simple and compound interest for the first conversion period are identical. The gap opens only from the second period, when compound interest starts charging interest on the first period's interest.
A handy shortcut for two years (annual compounding). The difference between compound and simple interest over exactly two years, at the same annual rate, is
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For the same P, R and T = 2 years compounded annually, CI - SI = P(R/100)^2, which is the second-year interest on the f …