IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Interest rates over different time periods
The force of interest is δ(t) = 0.04 for 0 ≤ t ≤ 5 and 0.06 for t > 5. A continuous payment stream at rate Rs 1,000 per annum runs from t = 0 to t = 10. Find the present value, to the nearest rupee.
Split the stream into two periods, discounting the second back at the earlier force. The total present value is about Rs 8,068.
- ARs 7,962Correct
- BRs 8,126
- CRs 7,415
- DRs 8,637
- Rs 7,000
Explanation
First 5 years: 1000×(1−e^-0.2)/0.04 = 1000×0.181269/0.04 = 4,531.7. Later: e^-0.2 × 1000×(1−e^-0.3)/0.06 = 0.818731×1000×0.259182/0.06 = 0.818731×4,319.7 = 3,536.7. Total = 8,068.4, which is not listed; the keyed option is not supported.
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