Microeconomics questions

1 Explain briefly how a life office calculates the new sum assured or annual premium on the

alteration or conversion of an existing policy.

A life office issued a whole life without profits policy to a woman aged 30, with sum assured of

110,000. Premiums were payable annually in advance throughout life, and the sum assured

was payable at the end of the year of death. Immediately before payment of the 15th premium,

the policyholder requests that the policy be converted to a without profits endowment assurance

for the same sum assured, payable on maturity at age 60 or at the end of the year of death, if

before age 60. The office calculates premiums and maintains reserves on the basis of A1967-70

ultimate mortality and 4% per annum interest, with expenses of 4% of each premium. Expenses

of alteration may be ignored.

Find the revised annual premium.

On 1 January 1972 an office issued a large number of 40-year endowment assurance policies,

each with sum assured 1000 (payable at the end of the year of death, if this occurs within the

term) to a group of lives all then aged 25. On 31 December 1988 there were 8567 policies still

in force. During 1989 there were 13 deaths among the policyholders.

Find the actual death strain, the expected death strain and the mortality profit or loss for the

business in 1989, using the following basis for all calculations:

mortality: A1967-70 select

interest: 4% p.a.

expenses: none

On 1 January 1991, a life office issued a number of identical special endowment assurances to

lives then aged 45. Each policy had a term of 15 years and level annual premiums were payable

throughout the term. On survival to the end of the term, a sum assured of 5000 is payable.

On death before the end of the term, a sum assured of 1000 is payable at the end of the year

of death and, in addition, all premiums paid are returned without interest.

The premium basis for these policies was as follows:

mortality: A1967-70 select

interest: 4% p.a.

expenses: Nil

(i) Show that the annual premium for each of these policies is 242.27.

(ii) Calculate the reserve, on the premium basis, on 1 January 1996 for one of these policies,

assuming that the premium then due is unpaid.

(iii) On 1 January 1995, a total of 10,000 of these policies were still in force. In 1995, 47

of these lives died, ten policies were surrendered, and the life office earned 4% interest

on its investments. Expenses were negligible in 1995. The surrenders all took place at

the end of 1995, and the office gave surrender values equal to 95% of the reserve on the

premium basis.

Calculate the profit or loss to the office in 1995 from this block of business in respect

A research chemist thinks he has discovered a new desiccant which is more efficient at extracting moisture from chemicals than the existing one. In order to test the claim, equal amounts of a homogeneously mixed compound are put into each of sixteen desiccators. These are divided into two batches of eight, labelled A and B, and in each batch the desiccators are numbered 1 to 8. Into each desiccator is also put a standard amount of the respective desiccant under test. Batch A contains the existing desiccant whilst the new desiccant is placed in Batch B. The desiccators are sealed for 24 hours and then the increase in weight in grams of each of the sixteen samples of desiccant is measured. The results are: Sample number 1 2 3 4 5 6 7 8 Existing desiccant (A) 4.59 5.05 4.49 5.33 4.66 4.98 5.67 5.23 New desiccant (B) 4.75 5.03 4.66 5.56 4.90 4.88 5.80 5.33 [A=40.0 _A2 =201.1574 _B=40.91 _B' = 210.3659 (i) (a) (1) Draw a plot of the data and comment briefly. (2) Perform a test to verify that the variances arising from the use of each desiccant are not significantly different and comment briefly in relation to your plot of the data. (b) Use a ttest to investigate the claim that the new desiccant extracts more moisture than the existing one. [8] (ii) It was subsequently discovered that eight different compounds had been used in the above test. The / th pair of desiccators A and B had contained equal weights of compound i, /=1,2,...,8. Perform a new analysis with the same aim, as in part (i)(b) above, again using a t test. [5] (iii) Comment on any difference found between the analyses, and the cause. [2] [Total 15]