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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Present value and accumulated value of cashflow streams

A loan of Rs 1,00,000 is repaid by two payments: Rs 60,000 at the end of year 1 and Rs X at the end of year 2. The effective annual rate of interest is 10%. Which value of X clears the loan exactly?

X is Rs 55,000. After the first payment the outstanding balance is 110,000 − 60,000 = 50,000, and one more year of 10% interest makes the final payment 55,000. Rs 50,000 ignores that final year's interest.

  1. ARs 40,000
  2. BRs 44,000
  3. CRs 50,000
  4. DRs 55,000Correct
  5. Rs 60,000

Explanation

Equation of value at time 0: 100,000 = 60,000/1.1 + X/1.21. 60,000/1.1 = 54,545.45, leaving 45,454.55. Multiplying by 1.21 gives X = 55,000. Check: the balance after year 1 is 110,000 − 60,000 = 50,000, which grows to 55,000. The value 50,000 wrongly ignores the second year's interest.

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