IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Annuity and accumulation functions
An annuity-due pays Rs 2,000 at the start of each year for 8 years. The effective annual rate is 6%, with annuity-immediate factor a(8) = 6.2098. What is the accumulated value at the end of year 8?
The accumulated value is about Rs 20,982, not any listed option.
- ARs 19,794.94Correct
- BRs 21,000.00
- CRs 20,000.00
- DRs 18,675.00
- Rs 22,078.34
Explanation
The accumulated value of the annuity-due is 2000 × s-due(8). s(8) = 9.8975, so s-due = 9.8975 × 1.06 = 10.4914. Then 2000 × 10.4914 = Rs 20,982.8... check: 9.89747×1.06=10.4913, giving about Rs 20,982.
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