IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Interest rates over different time periods
The force of interest is a constant 5% per annum for the first 4 years and 7% per annum thereafter. What is the accumulated value at time 10 of Rs 1,00,000 invested at time 0, to the nearest rupee?
Sum the force of interest over time: 0.05 times 4 plus 0.07 times 6 equals 0.62. Accumulating gives 100,000 times e^0.62, about Rs 1,85,893. This value is not among the options, so the question is flawed.
- ARs 1,64,872
- BRs 1,82,212
- CRs 1,97,730
- DRs 2,01,375Correct
- Rs 2,22,554
Explanation
The integral is 0.05×4 + 0.07×6 = 0.20 + 0.42 = 0.62. The accumulated value is 1,00,000 × e^0.62 = 1,00,000 × 1.858928 = 1,85,893. This does not match any option, so the key is inconsistent.
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