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

Priya takes a one-year loan of Rs 100,000. The lender deducts an arrangement fee of Rs 2,000 at the outset, so she receives Rs 98,000. She repays Rs 105,000 at the end of the year. What is the APR on the amount actually received, to two decimal places?

The APR is 7.14%. Priya actually receives Rs 98,000 and repays Rs 105,000 after one year, so the effective annual rate solves 98,000(1+i) = 105,000, giving i of about 7.14%. The fee raises the cost above the 5% stated rate.

  1. A2.94%
  2. B5.00%
  3. C7.00%
  4. D7.14%Correct
  5. 7.50%

Explanation

The equation of value is 98,000(1+i) = 105,000. So i = 105,000/98,000 - 1 = 7.14%. The 5.00% option ignores the fee. The 7.00% option adds the fee as 2% to the 5% stated rate, which uses the wrong base. The 2.94% option measures the interest against Rs 102,000.

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