Sorry if this is in the wrong forum, I just finished an exam at University and even with the study material and lecture notes I can't seem to solve this question, if anyone would let me know how it's done, or what my next steps should be I'd appreciate it. The question A life office issues a 10-year endowment assurance policy to a male life aged 40 exact. The sum assured of £10,000 is payable immediately on death and premiums are payable annually in advance for the term of the policy or until his earlier death. a) Calculate to 2 decimal places, the annual premium given: Interest 3% per annum The annuity (no idea how to insert it on here) part for the premium = 8.608 at 3% per annum interest Expenses nil b) Calculate to 2 decimal places, the prospective reserve of this policy on the premium basis after 3 years given (the annuity after 3 years, lasting 7 more years) = 6.329 My working out is as follows for part a And then that's where I got stuck, I can't find a way to value the pure endowment part without using any sort of tables or conversions.
I think you can use the equation: to get a value of the corresponding "annuity factor" payable continuously. This can then be used to derive the corresponding "assurance factor" function using:
Just a small correction to @KaustavSen's response here. The relationship between a-bar and a-due given above only works for whole life annuities. For example, we could use: \[ \require{enclose} {}\bar{a}_{40} \approx {}\ddot{a}_{40} - \frac{1}{2} \] However, if you have an annuity with a defined term (10 years in this question), then we need to use the following relationship: \[ \require{enclose} {}\bar{a}_{40:\enclose{actuarial}{10}} \approx {}\ddot{a}_{40:\enclose{actuarial}{10}} - \frac{1}{2} ( 1-v^{10} {_{10}p_{40}} ) \] Or, in general: \[ \require{enclose} {}\bar{a}_{x:\enclose{actuarial}{n}} \approx {}\ddot{a}_{x:\enclose{actuarial}{n}} - \frac{1}{2} ( 1-v^{n} {_{n}p_{x}} ) \]
I'm pretty sure you'd need to be given some additional information to use for calculating the npx values here, unless I'm missing something!