IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Annuity and accumulation functions
A perpetuity-immediate pays Rs 6,000 a year, the first payment being one year from now. The effective annual interest rate is 8%. What is its present value?
The present value is Rs 75,000. A perpetuity-immediate is worth the annual payment divided by the effective annual rate, so 6,000 divided by 0.08 gives 75,000. The due value would be higher because payments start immediately.
- ARs 48,000.00
- BRs 75,000.00Correct
- CRs 81,000.00
- DRs 7,500.00
- Rs 6,000.00
Explanation
PV of a perpetuity-immediate = payment / i = 6,000 / 0.08 = Rs 75,000. Rs 81,000 is the perpetuity-due value (75,000 x 1.08), which applies if the first payment were made today.
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