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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 100,000 carries interest at 10% effective per annum and is repaid by level annual payments of Rs 20,000 at the end of each year. How much capital is contained in the third payment?

The third payment contains Rs 12,100 of capital. The balance after two payments is Rs 79,000, so interest is Rs 7,900 and the remaining Rs 12,100 of the Rs 20,000 payment repays capital.

  1. ARs 7,900
  2. BRs 11,000
  3. CRs 12,000
  4. DRs 12,100Correct
  5. Rs 13,310

Explanation

Year 1: interest 10,000, capital 10,000, balance 90,000. Year 2: interest 9,000, capital 11,000, balance 79,000. Year 3: interest 7,900, so capital = 20,000 - 7,900 = 12,100. Rs 7,900 is the interest portion, not the capital.

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