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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Time value of money: compound interest and discounting

Meera invests ₹10,000 at 10% per annum. The bank uses compound interest for complete years and simple interest for any fraction of a year. What is the amount payable if she withdraws after 2.5 years?

The amount payable is ₹12,705. The bank compounds for 2 complete years to reach ₹12,100, then adds simple interest for half a year at 10%, giving 12,100 × 1.05 = ₹12,705. Fully compound accumulation would give a slightly lower ₹12,690.35.

  1. A₹12,690.35
  2. B₹12,500.00
  3. C₹12,750.00
  4. D₹12,100.00
  5. ₹12,705.00Correct

Explanation

After 2 complete years: 10,000 × 1.1^2 = 12,100. For the extra half year, simple interest applies: 12,100 × (1 + 0.10 × 0.5) = 12,100 × 1.05 = ₹12,705. Pure compounding, 12,100 × 1.1^0.5, gives ₹12,690.35, which is not the bank's method here.

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