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A bank offers 8% per annum on a ₹25000 deposit for 1 year. Under its simple-interest plan the rate is applied once; under its compound plan the interest is compounded half-yearly. How much MORE interest does the compound plan pay?

Class 8Comparing QuantitiesComparing Quantities
  • A₹0
  • B₹80
  • C₹40
  • D₹2040

Step-by-Step Solution

Simple: SI = . Half-yearly: 4% for 2 periods, so and CI = 2040. Difference = 40. Trap: ₹0 assumes CI always ties SI over one year — true for ANNUAL compounding, but here ₹1000 of interest is added after six months and itself earns 4% = ₹40. ₹2040 is the compound interest, not the gap.
Answer: C) ₹40

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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