# Return of premiums without interest

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Hi

Why is the increasing term assurance function used to calculate EPV of premiums returned without interest, rather than P + 2P*(1P60) + 3P*(2P60) + .... ? How would one calculate it if total premiums paid were to be returned with interest?

Thanks

by (2.9k points)

Firstly, just a small fix in your expression but it the P's should be replaced with Q's as these are death benefits being paid, not an annuity of the premiums.

The premiums paid are without interest but they still need to be discounted (hence why the increasing assurance is used). So, for your expression, you still need to discount those cashflows (even though the premiums don't increase with interest) which would result in the same expression as seen in the memo.

A good question! I like your curiosity! Well, if you did include interest in the premiums being paid back, the nominal amounts paid on each time period would be:

P*(1+0.04) + 2P*(1+0.04)^2 + 3P*(1+0.04)^3 + ....

We then take into account discounting the cashflows and mortality, and the final expression looks like:

P*(1+0.04)*(q_60)*(1+0..04)^-1 + 2P*(1+0.04)^2*(q_61*p_60) *(1+0..04)^-2+ 3P*(1+0.04)^3 *(q_62*2_p_60)*(1+0..04)^-3+ ....

=>P(q_60) + 2P*(q_61*p_60)+ 3P *(q_62*2_p_60)+ ....

Which you would likely solve by hand as this is just 5 years and you could use the table (unless you can think of a better/faster way to calculate this expression).

by (1.1k points)
Oh okay I see, thank you Murray!