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

A Delhi lender advances Rs 1,00,000 for one year at a nominal 12% per annum convertible monthly, with interest accumulated and repaid in one lump sum at the end of the year. A processing fee of 2% of the loan is deducted from the amount paid out. What is the APR, as an effective annual rate on the sum actually received, to two decimal places?

The APR is 14.98% per annum. The lump sum repaid is Rs 112,682.50, since 1% a month compounds over twelve months. The borrower actually receives only Rs 98,000 after the fee. Dividing repayment by receipt and subtracting 1 gives 14.98%, above the 12.68% effective rate that ignores the fee.

  1. A12.68%
  2. B14.00%
  3. C14.98%Correct
  4. D14.68%
  5. 12.00%

Explanation

The repayment is 100,000 x 1.01^12 = 112,682.50. The borrower receives 98,000. The APR is 112,682.50/98,000 - 1 = 14.98%. The 12.68% option ignores the fee, and 14.00% wrongly adds the 2% fee to the 12% nominal rate.

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