Compound bonus Q

[Barb37]

i am stuck on a calculation which involves compounding bonus.hope someone can help.

say, a endowment assurance policy with sum assured of 1 and reversionary compound bonus of 2% evaluates at 4% interest rate.
policyholder aged x
i can write the expected PV as Ax:n*j and j = (1.04)/1.02 - 1

is there a way to calculate this benefit explicitely?

many thanks and happy new year.

Barb

 

[John Potter]

Compound bonus

Barb37,

Your working seems spot on to me. Ax:n *j% where j = 1.04/1.02-1

None of the functions in the Yellow Tables are calculated at 2% so you would have to go back to frist principles:

Ax:n = {v dx + v^2 dx+1 + v^3 dx+2 +....+ v^n dx+n-1} / lx + v^n lx+n / lx

Notice how useful the dx's are here. You may have wondered why would there be a need for such a commutation function. Well, presumably, before computers, actuaries calculated Ax:n with a table of dx's in front of them, exactly like this!

I can't see this being asked in the CT5 exam for n>5 - it would be a test of who is fastest on the calculator.

Happy New Year!
John

 

[John Potter]

Compound bonus

Barb37,

Your working seems spot on to me. Ax:n *j% where j = 1.04/1.02-1

None of the functions in the Yellow Tables are calculated at 2% so you would have to go back to frist principles:

Ax:n = {v dx + v^2 dx+1 + v^3 dx+2 +....+ v^n dx+n-1} / lx + v^n lx+n / lx

Notice how useful the dx's are here. You may have wondered why would there be a need for such a commutation function. Well, presumably, before computers, actuaries calculated Ax:n with a table of dx's in front of them, exactly like this!

I can't see this being asked in the CT5 exam for n>5 - it would be a test of who is fastest on the calculator.

Happy New Year!
John