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

A borrower receives Rs 10,000 and repays Rs 5,500 at the end of year 1 and Rs 6,050 at the end of year 2. What is the APR (effective annual rate)?

The APR is 10.00%. Discounting the two repayments at 10% gives 5,000 + 5,000 = 10,000, which exactly equals the amount borrowed, so the equation of value is satisfied. Simple-interest shortcuts give lower answers because they ignore the repayments made earlier.

  1. A7.75%
  2. B9.09%
  3. C10.00%Correct
  4. D10.50%
  5. 15.50%

Explanation

At 10%, the present value is 5,500/1.1 + 6,050/1.21 = 5,000 + 5,000 = 10,000, which equals the loan, so i = 10%. The 7.75% option uses total interest of 1,550 divided by 2 years and by the loan, which is a simple-interest approach. The 15.50% option is total interest over the loan with no annualisation.

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