Problem 6: Assume that a cohort life-table population satisfies $l_0 = 10^4$ and
$d_x = egin{cases} 200, & \text{for } 0 \le x \le 14, \\ 100, & \text{for } 15 \le x < 48, \\ 240, & \text{for } 49 \le x \le 63. \end{cases}$
(a) Suppose that an insurer is to pay an amount $100(64 - X)$ (without regard to interest or
present values related to the time-deferral of the payment) for a newborn in the life-table. If
$X$ denotes the attained integer age at death, what is the expected amount to be paid?
(b) Redo (a) if the insurance is purchased for a life currently aged exactly 10.
(c) Find the expected present value at 4% interest of a payment of $1000 to be made at the
end of the year of death of a life currently aged exactly 20.