IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Present value and accumulated value of cashflow streams
The force of interest is a constant 6% per annum. Money is paid continuously at a constant rate of ₹1,000 per annum for 5 years into an account. What is the present value of this payment stream at time 0?
The present value is ₹4,319.70. For a level continuous payment stream, the present value equals the rate of payment times (1 − e^(−δn)) divided by δ. With δ = 0.06 and n = 5 this gives 1000 × 0.259182/0.06.
- A₹3,704.09
- B₹4,212.36
- C₹4,319.70Correct
- D₹5,000.00
- ₹5,830.98
Explanation
PV = 1000 × (1 − e^(−δn))/δ = 1000 × (1 − e^(−0.3))/0.06 = 1000 × 0.259182/0.06 = 4,319.70. The figure 5,830.98 is the accumulated value at time 5, so it is the wrong time point. The figure 4,212.36 uses an effective annual rate of 6% instead of a force of interest of 6%.
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