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

A loan of Rs 1,00,000 is granted at 10% per annum effective and is repaid by three level instalments paid at the end of each year. What is the annual instalment, to the nearest paisa?

The level instalment is Rs 40,211.48. It is found by dividing the loan by the three-year annuity-immediate factor at 10%, which is 2.486852. Using an annuity-due factor, or simply dividing the loan by three, ignores the timing of payments and gives a wrong figure.

  1. ARs 33,333.33
  2. BRs 36,555.89
  3. CRs 36,666.67
  4. DRs 40,211.48Correct
  5. Rs 43,333.33

Explanation

The instalment P satisfies P × a(3) = 1,00,000 at 10%. a(3) = (1 − 1.1^-3)/0.1 = 2.486852, so P = 1,00,000/2.486852 = 40,211.48. The figure 36,555.89 comes from wrongly using an annuity-due factor (2.735537), which assumes payments at the start of each year.

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