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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 is repaid by two payments, at the end of year 1 and at the end of year 2. The second payment is twice the first. The effective annual interest rate is 10%. What is the second payment, to two decimal places?

The second payment is Rs 78,064.52. Setting the present value of X at year 1 and 2X at year 2 equal to 100,000 gives X = 39,032.26, and doubling it gives the second payment.

  1. ARs 39,032.26
  2. BRs 57,619.05
  3. CRs 73,333.33
  4. DRs 78,064.52Correct
  5. Rs 82,644.63

Explanation

Let the first payment be X. Then X/1.1 + 2X/1.21 = 100,000. Multiplying by 1.21 gives 3.1X = 121,000, so X = 39,032.26 and the second payment is 78,064.52. Rs 39,032.26 is only the first payment. Discounting both at one year gives 73,333.33.

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