Hello Bharti,
I believe what the core reading is trying to imply is that the actual "
definition" of \(a_x\) is that it is the
Expected Present Value of an annuity payable annually in arrears until the life currently aged \(x\) is alive, ie,
\[
a_x = \mathbb{E}[a_{\overline{K_x}|}]
\]
However, if we simplify the expression we arrive at the formula that you have highlighted in the attached image. So, technically it is not a definition of \(a_x\) but what a formula to find the underlying value.
So, if in the exam we are asked to define \(a_x\), I believe we would be required to given its "definition" in terms of Expected Present Value and
NOT simply quote the formula.
Hope this makes sense to you. Please let me know if I missed out on anything. Again, these are just my interpretation and they may be wrong
.
Regards,
Kaustav.
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