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  • Clueless in this problem

    This is a problem involving fully discrete net premiums.

    An insured buys a whole life insurance policy with an initial benefit of 1. The interest rate is 4%. The insured's net premiums and death benefit are scheduled to increase each year at a compound rate of 4%. The death benefit is payable at the end of the year of death. Calculate the net premium payable at the beginning of the first policy year.

    How did it become Premium = v / (1 + ex)

    where v is the discount factor and ex is the curtate expectation of life?

  • #2
    If you write out the APV of the premium term by term, you
    get P[1 + v(1+i) px + v^2 (1+i)^2 2px + ... ] .
    v(1+i) = 1 since both interest rates are 4% , similarly
    v^2 (1+i)^2 = 1 , etc. The sum becomes
    P[1 + px + 2px + ...] = P[1 + ex] .

    The APV of the benefit simplifies in a similar way.
    v qx + (1+i) v^2 1|qx + (1+i)^2 v^3 2|qx + . . .
    =v [ qx + 1|qx + 2|qx + . . . ] = v(1) .
    qx + 1|qx + 2|qx + . . .= (1-px) + (px - 2px) + (2px - 3px) + ... = 1.

    Sam Broverman
    Sam Broverman

    [email protected]
    www.sambroverman.com

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