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The annual fee at a Bhopal coaching centre is ₹8000 and rises by 10% every year. By how many rupees will the fee have gone up in total after two such rises?

Class 8Comparing QuantitiesComparing Quantities
  • A₹1600
  • B₹800
  • C₹1680
  • D₹9680

Step-by-Step Solution

Year 1: . Year 2: . Total rise = 9680 − 8000 = 1680. Trap: taking 10% of the original ₹8000 twice gives ₹1600 — that is simple-interest thinking, which misses the second rise being charged on the already-raised fee. ₹9680 is the new fee, not the rise.
Answer: C) ₹1680

Key idea: Compound interest — interest on interest

After year 1, interest is added to principal — so year 2's interest is calculated on a LARGER amount, not the original.

****, where A is the final amount after years.
**CI = ** (the total interest earned).

Example: ₹2000 at 5% for 3 years, compounded annually:
- Year 1: Year 2: Year 3:

Direct formula: . CI = 2315.25 − 2000 = 315.25 (vs SI of 300 — compound gives more).

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