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

Rohan borrows Rs 2,00,000 from a bank, repayable by level annual instalments at the end of each year for 5 years at 10% per annum effective. What is the annual instalment, to the nearest rupee? (a-bar value: a(5) at 10% = 3.790787)

The level instalment equals the loan divided by the five-year annuity-immediate factor at 10%. Dividing 2,00,000 by 3.790787 gives about Rs 52,759. Simply dividing the loan by five ignores interest, and adding simple interest overstates the instalment.

  1. ARs 40,000
  2. BRs 52,759Correct
  3. CRs 54,000
  4. DRs 48,000
  5. Rs 60,000

Explanation

Equation of value: 200000 = X * a(5) at 10% = X * 3.790787, so X = 52,759.50, about Rs 52,759 (rounded down to 52,759.5 gives 52,759 or 52,760). The option Rs 40,000 ignores interest (200000/5), and Rs 54,000 adds only simple interest on the opening balance.

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