2.8 Comparing SI and CI Growth Over Time
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Figure: Simple Interest grows in a straight line; Compound Interest curves upward as interest earns interest.
Because SI grows linearly while CI grows exponentially, the two are always equal at the end of year 1 (with annual compounding, since no compounding has occurred yet) and CI overtakes SI from year 2 onwards, with the gap widening every year. Illustration for P = Rs. 10,000 at R = 10% p.a.:
| Year | Amount at SI | Amount at CI | Extra earned by CI |
|---|---|---|---|
| 1 | 11,000 | 11,000 | 0 |
| 2 | 12,000 | 12,100 | 100 |
| 3 | 13,000 | 13,310 | 310 |
| 4 | 14,000 | 14,641 | 641 |
| 5 | 15,000 | 16,105.10 | 1,105.10 |
This table is worth memorising conceptually: CI = SI only in year 1; after that, CI is always strictly greater, and the excess for any year n equals the CI on all the “interest-on-interest” accumulated so far. This is the basis of many comparison-based MCQs that ask “for how many years will CI exceed SI by more than Rs. X.”