MATH 273 Life Insurance Mathematics I 2021-2022
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CLASS TEST 2 2021-2022
MATH 273
Life Insurance Mathematics I
1. Given
1200 - 12x
1200
(i) What is the implied limiting age ω? [2 marks]
(ii) Calculate l北 for x = 0, 1, 2, ...ω - 1 , with l0 = 10, 000. [2 marks]
(iii) Calculate the values for p北 for x = 0, 1, 2, ...ω - 1, with l0 = 10, 000. [2 marks]
(iv) Calculate e70 . [2 marks]
2. You are given the following life table extract
|
x |
|
|
65 |
79,950 |
|
66 |
79,078 |
|
67 |
77,892 |
|
68 |
76,334 |
|
69 |
74,426 |
|
70 |
72,193 |
(i) Calculate 
65:5
using an effective interest rate of 2% [2 marks]
(ii) Calculate 
using an effective interest rate of 2%. [2 marks]
(iii) Briefly discuss the results you got in part (i) and (ii). [2 marks]
(iv) Calculate (IA)6(1)5:5
using an effective interest rate of 2%. [3 marks]
3. An insurer issues a 30-year endowment insurance policy to a life aged 50. The sum insured of f15,000 is payable at the end of the year of death or on survival. Level premiums are payable annually throughout the term.
Premium and Policy Value basis
● Survival model: q50+t = 0.001t + 0.012 with l50 = 10, 000
● Interest: 1% per year.
● Level premiums are calculated using the equivalence premium.
(i) Calculate the annual premium using the equivalence principle. [3 marks]
(ii) Calculate the policy values, t V , for t = 0, 1, ..., 30 − using commuta- tional functions. [3 marks]
(iii) Draw a graphic of t V and comment on your results. [2 marks]
(iv) Calculate the annual premium for the 30-year term insurance, i.e. if the survival benefit is eliminated. [2 marks]
(v) Calculate the t V for the 30-year term insurance and draw a graphic. Comment on your results. [3 marks]
2023-01-11