IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Interest rates over different time periods
Which expression gives the force of interest δ(t) in terms of the accumulation function A(t)?
The force of interest is the instantaneous proportional rate of growth of the accumulation function, A'(t) divided by A(t), which equals the derivative of ln A(t).
- AA'(t)
- BA'(t)/A(t)Correct
- CA(t)/A'(t)
- Dln A(t)
- A''(t)/A'(t)
Explanation
The force of interest is the proportionate rate of growth of the fund, δ(t) = A'(t)/A(t) = d/dt ln A(t). Option ln A(t) is the integral of δ, not δ itself. A'(t) alone is the absolute rate of growth.
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