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

An investor buys a 9-month bill with maturity value ₹1,00,000 at a price of ₹92,500, being discounted at a simple discount rate of 10% per annum. What is the investor's effective annual compound rate of return, to two decimal places?

The effective annual return is 10.95%. The bill costs ₹92,500 and pays ₹1,00,000 nine months later, a growth factor of 1.081081. Raising this to the power 12/9 gives about 1.1095. The 10.81% figure is merely the simple annualised yield.

  1. A10.00%
  2. B10.81%
  3. C11.25%
  4. D10.95%Correct
  5. 8.11%

Explanation

Price = 100,000 × (1 − 0.10 × 0.75) = 92,500. Growth over 9 months = 100,000/92,500 = 1.081081. Annual effective = 1.081081^(12/9) = exp(1.3333 × 0.077961) = 1.10954, so 10.95%. The 10.81% option is only the simple annualised yield (0.081081/0.75), ignoring compounding.

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