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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Practical applications of the equation of value (loans and APR)

Meera takes a Rs 50,000 loan at a 10% per annum flat (simple) rate, with the whole amount including interest repaid in a single payment at the end of 2 years. What is the effective annual rate of interest, to two decimal places?

The effective annual rate is 9.54%. Repayment after two years is Rs 60,000, which is 1.2 times the loan. Solving (1+i)^2 = 1.2 gives i = 9.54%. Because there are no intermediate repayments, the effective rate is below the 10% flat rate.

  1. A10.00%
  2. B9.54%Correct
  3. C9.09%
  4. D20.00%
  5. 9.80%

Explanation

Repayment = 50,000 × (1 + 0.10 × 2) = 60,000. The effective rate satisfies (1+i)^2 = 1.2, so i = sqrt(1.2) − 1 = 1.09545 − 1 = 9.54%. The 10% figure wrongly treats the flat rate as effective, and 20% is the two-year total rate.

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