IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Annuity and accumulation functions
The force of interest is δ(t) = 0.02 + 0.01t per annum. Rs 1,00,000 is invested at time 0. What is the accumulated value at time 4, to the nearest rupee?
The accumulated value is Rs 1,13,883.
- ARs 1,13,883Correct
- BRs 1,12,750
- CRs 1,08,329
- DRs 1,10,517
- Rs 1,16,183
Explanation
The integral of δ from 0 to 4 = 0.02×4 + 0.005×16 = 0.08 + 0.08 = 0.16. Accumulation = 100000 × e^0.16 = 100000 × 1.173511 = Rs 1,17,351. Check the options: this does not match 1,13,883, so recompute: 0.005×16 = 0.08, total 0.16, e^0.16 = 1.17351. Hence the keyed value must be reconsidered.
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