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MLC Problem on Gross premiums

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  • MLC Problem on Gross premiums

    Hoping someone can help me with this. The question reads:

    For a fully discrete whole life insurance of 10,000 on (45):
    (i) Both net and gross premiums are reduced by half starting with the 21st premium.
    (ii) Expenses are 50% of premium in the first year, 10% of premium in renewal years.
    (iii) A_45 = .15, A_65 = .24, A_75 = .4
    (iv) d = .04
    (v) 20_p_45 = .9
    (vi) 30_p_45 =.75

    Calculate the expense reserve at time 30.

    I proceded to get 78.5221 for the gross premium. Looking in the back of the book, however, I see they get 97.89. For the calculation, they show:

    G = 1500/ ( .9 (21.25 - .5(7.5582) ) - .4 ) = 97.89

    21.25 is a life annuity on (45) due
    7.5582 is a 20 year deferred life annuity due on (45)
    1500 is the expected insurance payment.

    It seems as though the author is saying, since premiums are reduced by half, we just take a whole life annuity and subtract a half a deferred annuity. The .9, though, looks like a typo to me. Am I right, or am I missing a vital piece of understanding?
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