IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Annuity and accumulation functions
A perpetuity-due of Rs 600 per year has a present value of Rs 10,600 at an effective annual rate i. What is i?
The rate is 6.00%. A perpetuity-due is worth the payment times (1 + 1/i), so 10,600/600 − 1 = 16.6667 equals 1/i. Dividing 600 by 10,600 gives 5.66%, which wrongly treats it as an immediate perpetuity.
- A5.66%Correct
- B6.00%
- C5.00%
- D6.38%
- 10.00%
Explanation
Perpetuity-due PV = 600(1 + 1/i) = 10,600, so 1/i = 10,600/600 − 1 = 16.6667, giving i = 6.00%. Therefore option 6.00% is correct; 5.66% comes from dividing 600 by 10,600, which ignores the immediate first payment.
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