A life insurance company sells whole-life assurance policies with a sum assured of $20,000, payable at the end of the ye

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A life insurance company sells whole-life assurance policies
with a sum assured of $20,000, payable at the end of the year of
death. A life aged 50 exact has just committed to purchase a policy
(first premium not paid yet). The premium is $420 payable annually
in advance until the death of the policyholder.
a) Find the expected present value of the future loss to the
company arising from this policy.
b) Show that the variance of the present value of the future
loss from this policy can be expressed as 𝑏. 𝐴50 ′ + 𝑐. Determine
the numerical values of 𝑏 and 𝑐, and the rate of interest used to
evaluate 𝐴50 ′ . Basis: mortality AM92 Ultimate, interest 4% pa.
Ignore expenses.