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A deposit of ₹30000 made by Deepak has grown to ₹36300 after 2 years of annual compounding. Find the rate of interest per annum.

Class 8Comparing QuantitiesComparing Quantities
  • A21%
  • B10.5%
  • C20%
  • D10%

Step-by-Step Solution

, so → → → %. Trap: 21% is the total growth over BOTH years, and halving it to 10.5% is simple-interest thinking — with compounding the second year earns on a bigger base, so the yearly rate is a little under half the two-year growth.
Answer: D) 10%

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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