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

A debt of Rs 12,000 due at the end of year 3 is to be settled by paying Rs 5,000 now and a payment X at the end of year 2. At an effective annual rate of 10%, what is X?

X is Rs 4,859.09. Setting the present values equal, 12,000 discounted three years is Rs 9,015.78. Subtracting the Rs 5,000 paid now leaves Rs 4,015.78 at time 0, which must be accumulated two years at 10% to give the year-2 payment.

  1. ARs 4,859.09Correct
  2. BRs 7,000.00
  3. CRs 4,015.78
  4. DRs 5,909.09
  5. Rs 4,417.36

Explanation

Equation of value at time 0: 5,000 + X/1.21 = 12,000/1.331 = 9,015.78. So X/1.21 = 4,015.78 and X = 4,015.78 × 1.21 = 4,859.09. Rs 4,015.78 forgets to accumulate the present value to time 2. Rs 7,000 ignores interest.

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