Reserve Question (C3)

[Girl]

Can someone please help me with the following.... this is from the May2000 exam #9

For a 10 year deferred whole life annuity of 1 on (35) payable continuously:
mortality follows De Moivre's law with w = 85
i = 0
level benefit premiums are payable continuously for 10 years

calculate the benefit reserve at the end of 5 years.


SO - my work would be probably longer (and I don't get the right answer) but I don't understand the way they set up the solution. In the solution they don't have any benefits - just the premiums! Am I missing something? I would have used the prospective formula and then PVFB-PVFP.

Thanks for any help!

[retaker]

They are probably using the prospective method.

[retaker]

"level benefit premiums are payable continuously for 10 years"

Never mind. He he :)

[Bama Gambler]

Think retrospective!! Restrospective reserve = accum value of premium - accum value of benefits. But the accum value of benefits = 0 because this is a 10 year deferred whole life annuity. In other words, at time t = 5 no benefit have occured. First lets find the benefit premium. Benefit Premium = 10 year deferred annuity for a 35 year old / 10 year temporary annuity for a 35 year old (i.e. what you get / what you have to pay). This problem is MUCH easier b/c i = 0. The present value of the 10 year deferred annuity becomes (v^10)*Prob 35 yr old lives to 45*complete expectation of life for a 45 year old. The present value of 10 year temporary annuity (with i = 0) = the complete expectation of life for a 35 year old limited to 10 years. Now that you have P (the benefit premium) you must accum it for 5 years = 5 V = P s bar 35:5 = P a bar 35:5 / 5 E 35. As we did before a bar 35:5 = e circle 35:5 because i = 0. And 5 E 35 = 3 p 35.

Hope this helps.
Bama Gambler

[Girl]

Thanks Bama! That really does help me. I just wish I could start thinking like that!!

Any time I think of a reserve - my mind automatically goes to prospective method.

Thanks again!

[Bama Gambler]

Thanks Bama! That really does help me. I just wish I could start thinking like that!!

Any time I think of a reserve - my mind automatically goes to prospective method.

Thanks again!

No problem. I used to be the same way. There are actually 8 ways to think about reserves: Prospective, in terms of annuities, in terms of insurance, in terms of benefit premiums, difference in premiums, paid up reserves, retrospective, and then what Batten calls the Special Reserve Formula (I don't know what the book calls it).

Basically the Special Reserve formula says take your reserve at time t add the premium you collect at the beginning of the period, then accum that for one year = the prob you die times the net amount at risk. The net amount at risk is the difference in the death benefit and the reserve. Another way to think about it is take your reserve at the beginning of the year add the premium accum it for a year (i.e. mult. by 1+i) set that equal to the death benefit times the prob. you die during the year + the reserve at the end of the year * prob. that you live. In other words, if you die you have to pay the death benefit, if you live you need to have next year's reserve.

Bama Gambler

[Girl]

Hey your good! Is this your first time writing this? (Or are you even writing 3?)

That helps too - I knew the recursive formula but couldn't really put it to words like that.

Thanks again!

[Bama Gambler]

Hey your good! Is this your first time writing this? (Or are you even writing 3?)

That helps too - I knew the recursive formula but couldn't really put it to words like that.

Thanks again!

Thanks. This is my first time to take course 3, but I attended a Bob Batten seminar. He really simplifies the concepts.