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A jeweller in Surat puts ₹40000 into a deposit scheme that pays 10% per annum, compounded every six months, and leaves it untouched for 18 months. What amount does he get back?

Class 8Comparing QuantitiesComparing Quantities
  • A₹46000
  • B₹46305
  • C₹44100
  • D₹53240

Step-by-Step Solution

Six-monthly compounding means 5% per period, and 18 months = 3 periods. . Trap: ₹53240 keeps the annual 10% for 3 periods instead of halving it, ₹44100 uses only 2 periods (12 months), and ₹46000 is what plain simple interest would give.
Answer: B) ₹46305

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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