IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Equation of value
An annuity-immediate pays Rs 1,000 at the end of each year for 5 years. Using an effective annual interest rate of 8%, what is its present value?
The present value is Rs 3,992.71. Each end-year payment of Rs 1,000 is discounted at 8%, giving 1000 × (1 − 1.08^-5)/0.08. The annuity-due figure of Rs 4,312.13 is wrong because the payments here are made at year ends.
- ARs 3,312.13
- BRs 3,992.71Correct
- CRs 4,312.13
- DRs 4,622.88
- Rs 5,000.00
Explanation
PV = 1000 × a(5) = 1000 × (1 − 1.08^-5)/0.08. Here v^5 = 0.680583, so a(5) = 0.319417/0.08 = 3.99271 and PV = Rs 3,992.71. Rs 4,312.13 is the annuity-due value, which wrongly treats payments as made at the start of each year.
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