IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Interest rates over different time periods
The force of interest is 6% per annum constant. Find the effective rate of interest over a half-year period, to two decimal places.
The effective half-year rate is 3.05%. With a constant force of interest of 6%, the accumulation over half a year is e raised to 0.03, which is 1.03045, giving an effective rate of about 3.05% over the half-year.
- A3.00%
- B3.05%Correct
- C3.09%
- D6.18%
- 2.96%
Explanation
Half-year accumulation = e^(0.06×0.5) = e^0.03 = 1.030455. Effective rate = 3.05%. The 3.00% option merely halves the force, and 6.18% is the annual effective rate.
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