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truth in lending
November 28th 2005, 12:54 PM
Hello...

What must be the formula of a (fully continuous) continuously decreasing 25-yr. term insurance issued to (40)? (only the benefit not the premium)


The benefit b_t = 1000a-(25-t) (1000 times a continuous annuity of 25-t... sounds like a "bar" "angle 25-t"), for 0 <= t <= 25.

i = 0.05, premium is 200

The problem is to find the net premium reserve at the end of 10 years for this insuramce. (the answer is given to be 800 to this problem)

Ken
November 28th 2005, 07:43 PM
I'm getting caught up in your notation.
How are you modeling the deaths?

truth in lending
December 2nd 2005, 12:58 PM
In getting my reserve,

{(integral from 0 to 15) my given benefit in the problem but instead of 0 <= t <= 25, I changed it into 0 <= t <= 15 (times) v^t tpx U_x+t dt } - 200 X (continuously 15-yr temporary life annuity for a person aged 50).

I am not sure if this is correct and if is understandable... I apologize.

Ken
December 2nd 2005, 02:26 PM
In getting my reserve,

{(integral from 0 to 15) my given benefit in the problem but instead of 0 <= t <= 25, I changed it into 0 <= t <= 15 (times) v^t tpx U_x+t dt } - 200 X (continuously 15-yr temporary life annuity for a person aged 50).

I am not sure if this is correct and if is understandable... I apologize.

{(integral from 0 to 15) 1000(1-v^(15-t))/delta v^t tpx U_x+t dt } - 200 X (continuously 15-yr temporary life annuity for a person aged 50).

I think you expand the integral and then integrate.

truth in lending
December 4th 2005, 10:49 AM
Hello Ken:

I think I can handle it from here. thank you for your time.