IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Annuity and accumulation functions
At 4% per annum effective, what is the present value of an annuity-due paying Rs 500 at the start of each year for 5 years? (v = 1/1.04; 1 − v^5 = 0.178073)
The present value is about Rs 2,314.96, found as 500 times the five-year annuity-due factor of 4.6299. The figure of Rs 2,225.91 is the annuity-immediate value and ignores payments being at the start of each year.
- ARs 2,225.91
- BRs 2,314.96Correct
- CRs 2,225.00
- DRs 2,500.00
- Rs 2,140.00
Explanation
d = 0.04/1.04 = 0.0384615. a-due(5) = 0.178073/0.0384615 = 4.62990. Multiply by 500 to get Rs 2,314.95 (about 2,314.96 with rounding). Rs 2,225.91 is the annuity-immediate value (500 × 4.45182).
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