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

A bank lends Rs 50,000 to a customer in Chennai. The loan is repaid by Rs 30,000 at the end of year 1 and Rs 30,000 at the end of year 2. What annual effective interest rate (the APR) is implied, to two decimal places?

The implied APR is 13.07% per annum. Setting the present value of the two Rs 30,000 repayments equal to the loan of Rs 50,000 gives a quadratic in v. Solving it gives v of 0.8844, so the interest rate is 1/v minus 1, which is 13.07%.

  1. A10.00%
  2. B12.00%
  3. C13.07%Correct
  4. D14.50%
  5. 16.00%

Explanation

Solve 50,000 = 30,000v + 30,000v^2, so v^2 + v - 5/3 = 0. Then v = (-1 + sqrt(7.6667))/2 = 0.884438, and i = 1/v - 1 = 13.07%. Check: 30,000/1.130661 + 30,000/1.278409 = 26,533 + 23,467 = 50,000. At 12% the present value would be 50,710, so 12% is not correct.

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