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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 repaid by level annual payments of Rs 26,380 at the end of each year for 4 years. The effective annual interest rate is 10%. What is the capital (principal) repaid in the second instalment, to the nearest rupee?

The second instalment's capital is Rs 18,018. After the first payment the balance is Rs 83,620, year-two interest is Rs 8,362, and subtracting this from the Rs 26,380 payment leaves Rs 18,018 as principal repaid.

  1. ARs 16,380
  2. BRs 18,018Correct
  3. CRs 20,000
  4. DRs 26,380
  5. Rs 10,000

Explanation

Interest in year 1 = 10,000, so capital repaid = 16,380 and the balance becomes 83,620. Interest in year 2 = 8,362, so capital repaid = 26,380 - 8,362 = 18,018. Rs 16,380 is the first instalment's capital, a common slip.

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