2016 April Q12

Hi guys, I'm confused with calculation of EPV of death benefit in the answer of 2016 April Q12i, 150000 * EAbar[45] @i'%.

I understand how to calculate the i'%, but shouldn't the formula be =150000/(1.0192308) * (1.06)^0.5 * EA[45] @i'%.
How come the compound bonus of 1.92308% is missing?

Thanks

 

It's a good idea to write out the EPV of benefits from first principles for these questions, so you can see exactly what's going on before simplifying things. For this question we have:

EPV bens = 150,000 * ( v^0.5*(1+b)*q[45] + v^1.5*(1+b)^2*p[45]*q[45]+1 + ...)

I've used b = 1.92308% above for ease (feel free to do this in the exam to save a bit of typing!). We want the powers of v and 1+b for the first term in the brackets to both be one if we're going to be able to use an assurance at 4% interest. We can do this by taking out a factor of 1.06^0.5:

EPV bens = 150,000*1.06^0.5 * ( v*(1+b)*q[45] + v^2*(1+b)^2*p[45]*q[45]+1 + ...)
= 150,000*1.06^0.5*A:[45]@4%

Which is the same as what's in the Examiners' Report.

(Very quick point on your notation - I'd probably use EA:[45] for an endowment assurance rather than a whole life assurance. I'd go with A:[45] or WA:[45] for a whole life assurance.)