Deriving formula for accumulated values of annuity

Question

Question 1) Describe the pure endowment insurance.

Question 2) Describe temporary assurance.

Question 3) Derive a formula for accumulated values of annuity.

Question 4) Explain level benefit insurance.

Question 5) Write a short note on endowment assurance.

Question 6) Explain deferred temporary life annuity.

Question 7) Find the value as at the end of 5½ years of an annuity of 120/- p.a payable half yearly for 20 years at the rate of interest being taken as 6% p.a convertible half yearly.

Question 8)a) Explain various aspects involved in insurance payable at the moment of death.

b) Determine the net single premium for 20years endowment assurance with sum assured 500 payable at moment of death for a select life aged 40 subject to the following information at 4% interest. Given M_[40] =1904.86  D_[40] =6981.60  M_[60] =1477.08 D_[60] =2885.59

Question 9)a)    The following particulars are given:

X      35         36        38        39        40       41        42       43       44
Lx    10000    9941    9907    9869    9827    9780    9728    9671    9608
dx    28          34       38         42        47       52       57        63       70

Compute the level annual premium for pure endowment assurance for 10 years on the life of a person aged 35 years for 10000 ignoring interest costs.

b) Derive the expression for accumulated value of immediate annuity of 1p.a

Question 11)a) Determine the present value of a series of 6 payments of  200 p.a. the first one being made at the end of 8 years assuming a rate of interest of 6% p.a.

Question 12)a) Describe

(i) Increasing temporary assurance

(ii) Increasing whole life assurance

b) Describe the use of communication functions D_x, C_x, M_x and R_x, giving suitable examples.