(a) Aga Khan, aged 45, takes out a whole-life assurance policy with a sum insured of £85,000 paid at the instance of death. Assume an effective interest rate of 4% per annum and mortality given by the AMC00 Select Table. (i) Show that the cost of the life assurance policy as a net single premium is approximately £22,169. State any approximations made. (ii) If he pays for the assurance annually in advance until his retirement at age 67, what is the annual premium? (iii) If he instead pays for the assurance by making monthly payments in advance until retirement, what is the monthly premium? Use the relationship
(a) Aga Khan, aged 45, takes out a whole-life assurance policy with a sum insured of £85,000 paid at the instance of death. Assume an effective interest rate of 4% per annum and mortality given by the AMC00 Select Table. (i) Show that the cost of the life assurance policy as a net single premium is approximately £22,169. State any approximations made. (ii) If he pays for the assurance annually in advance until his retirement at age 67, what is the annual premium? (iii) If he instead pays for the assurance by making monthly payments in advance until retirement, what is the monthly premium? Use the relationship
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Question 5
(a) Aga Khan, aged 45, takes out a whole-life assurance policy with a sum insured of
£85,000 paid at the instance of death. Assume an effective interest rate of 4% per
annum and mortality given by the AMC00 Select Table.
(i) Show that the cost of the life assurance policy as a net single premium is
approximately £22,169. State any approximations made.
(ii) If he pays for the assurance annually in advance until his retirement at age
67, what is the annual premium?
(iii) If he instead pays for the assurance by making monthly payments in advance
until retirement, what is the monthly premium? Use the relationship
äm=ä(?) - nä(?)
and state any approximations made.
(b) Consider the function Q defined as
00
Qz = (lz+j-lx+j+1) ²+j+1,
j=0
where is the expected number of survivors to age z. Show that in terms of Q,
we can express the cost of a £1 death benefit payable at the end of the year of
death as
Qz
D₂'
where D, is the usual commutation function D, =l₂v².
AT
=
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