IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Annuity and accumulation functions
A perpetuity pays Rs 1,000 at the end of year 1, Rs 2,000 at the end of year 2, Rs 3,000 at the end of year 3, and so on, increasing by Rs 1,000 each year for ever. At an effective rate of 5% per annum, what is its present value?
The present value is Rs 420,000. For an increasing perpetuity-immediate the unit value is 1/(i d), equal to (1+i)/i^2, which at 5% is 420. Multiplying by Rs 1,000 gives the answer. The figure 1/i^2 would be 400 and applies to a perpetuity starting one year later.
- ARs 400,000.00
- BRs 420,000.00Correct
- CRs 20,000.00
- DRs 441,000.00
- Rs 380,952.38
Explanation
For an increasing perpetuity-immediate, (Ia)∞ = 1/(i d) = (1+i)/i^2 = 1.05/0.0025 = 420. Multiplying by 1,000 gives Rs 420,000. Rs 400,000 is 1/i^2, which is one year too late. Rs 441,000 over-compounds by using (1+i)^2.
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