Chapter 20
Vocabulary:
Budget
o An accounting device used to plan and control resources of operational departments and
divisions
Capital expenditure budget
o The budget summarizing future plans for acquiring plant facilities and equipment
Cash budget
o

Chapter 12
Vocabulary:
Cash dividend
o A cash distribution of earnings by corporation to its shareholders
Common stock
o The stock outstanding when a corporation has issued only one class of stock
Cumulative preferred stock
o A class of preferred stock

Mortality: up to age 65: AM92 Select over age 65: PFA92C20 Interest:
4% pa Expenses: none [8] CT5: Q&A Bank Part 2 Questions Page 9
The Actuarial Education Company IFE: 2013 Examinations Question
2.22 A life office sold a portfolio of 10,000 term assuranc

given the following information: Reserve at the start of the 8th year
(per policy in force): 12,940 Number of policies in force at the start of
the 8th year: 200 Number of deaths during the 8th year: 3 Annual net
premium (per policy) 1,591 (i) Assuming th

declared at the rate of 1.92308% of the sum assured, compounded
and vesting at the end of each policy year on the following basis:
Mortality: AM92 Select Interest: 6% pa Initial expenses: 114% of the
first premium and 2.5% of the basic sum assured Renewal

result that follows from a uniform decrement assumption. [1] III is
false. The multipliers t and t -1 are transposed. For example, putting t
= 0 gives x x 1 l l = + , instead of x x l l = . [1] [Total 3] Page 4 CT5: Q&A
Bank Part 1 Solutions IFE: 2013 Exa

2013 Examinations Hence the premium is: 60:2| 798.88 608.29
1,407.17 720.21 1.953825 P a + = = [1] [Total 7] (ii) Net premium
reserve and mortality profit The net premium reserve is equal to the
value of future benefits less the value of net premiums. The

maturity value is 25,000. So the prospective net reserve is: 1 1 60 4
| | 54:6 54:6 54:6 54 13,000 1,000( ) 25,000 pro D V A IA Pa D = + +[2] where the premium is given by: 1 1 60 50:10 50:10 50:10 | | 50
9,000 1,000( ) 25,000 D Pa A IA D =+ + [2] [Total

100 0.03 ( 1) [2] The factors are: 44 [32]:12| [32] 44 [32] 1,747.41
21.523 19.075 9.726 2,825.48 D aa a D =- = - = [1] 1 44 [32]:12| [32]
44 [32] 1,747.41 0.17218 0.26636 0.00745 2,825.48 D AA A D =- = - =
[1] So the premium equation becomes: 9.726 5,000

Rearranging, dividing by h , and letting h 0 , gives the differential
equation: () ( ) () V t P S Vt =- + + mxt xt + + m d or: ( ) ( ) [ ( )] V t P Vt
S Vt =+ - - d mx t + [1] The second form separates the savings
element (the growth in the reserve ignori

Part 2 Solutions IFE: 2013 Examinations The Actuarial Education
Company Solution 2.2 The premium equation is: 1 32:12 32:12 | | Pa A
= 5,000 [1] The factors are: 44 32:12| 32 44 32 1,747.41 21.520 19.075
9.725 2,825.89 D aa a D =- = - = [1] 1 44 32:12| 32

Solutions Page 13 The Actuarial Education Company IFE: 2013
Examinations Solution 2.20 (i) Calculation of life table functions (a) We
have the relationship: 63 62 62 62 62 l lp l q = =- (1 ) [ ] So: 100,000 (1
0.0200) 62 = - l fi = l62 102,040.8 [ ] (b) W

benefits 3,000 3,000 3,000 ( ) = = - = - retro V D D a a D D D a a D [2]
Since the difference of annuities in the brackets represents the value
at age 60 of quarterly payments made in arrears for the 9 years
between ages 61 and 70, this can be written as:

[40]:25 [40]:25 1 1/ A da a d a a - = =- [1] CT5: Q&A Bank Part 2
Solutions Page 3 The Actuarial Education Company IFE: 2013
Examinations So the correct answer is: 1 / 1/ 1 ( 1) / a a a d da a 45:20
[40]:25 [40]:25 45:20 [40]:25 | | | | - + - = - - [1] [

2.28 A whole life assurance policy pays a benefit of 50,000 at the end
of the year of death. The policyholder is currently aged 30 and is
paying an annual premium of 700 at the start of each year. A
premium has just been paid. Use the following basis to c

birthday, by payment of a single premium. Show algebraically that the
current retrospective and prospective net reserves are equal assuming
that the premium and reserving bases are the same. Ignore expenses.
[4] Page 6 CT5: Q&A Bank Part 2 Questions IFE:

strain for year t +1 is the total death strain incurred in respect of all
claims actually arising during year t +1. 1 claims during year ADS for
year 1 ( ) += - t+ t SV [1] [Total 3] (ii) Mortality profit The net
premiums per unit sum assured for the thre

[35]:30 [35]:30 | | [35]:30| 65 [35] 12 205,000 5,000( ) 10,000 D Pa A
IA a D =-+ [2] The factors (calculated using the appropriate mortality
and interest rates) are: (12) 65 | [35]:30| [35]:30 [35] 11 11 1 17.631
0.72508 17.299 24 24 D a a D = - - = - =

reserve at the end of year 20 is: 30 1 20 | | | 30:20 30:20 30:20 50
30,000 100 0.05 ( 1) retro D V Pa A P a D = - - - [2] where the
premium is given by: Pa A P a 30 30 30 = + - 30,000 100 0.05 ( 1) [2]
[Total 4] CT5: Q&A Bank Part 2 Solutions Page 11 The

assured of 10,000 payable at the end of the year of death. Premiums
are calculated assuming AM92 Select mortality, 4% pa interest, initial
expenses of 150 and claim related expenses of 3% of the base sum
assured (payable on death or maturity). (i) Calcula

0.03 5 0.04 0.85 5 60 5 65 60:10 0.42741 - - - - A vpp e e e e = =
= [1] So the EPV of the endowment assurance is: 50,000 0.12363
0.67032 0.16105 0.42741 32,950 ( + =) [] [Total 1] CT5: Q&A
Bank Part 2 Questions Page 1 The Actuarial Education Company
IF

profit in part (ii) ignores the contingency loading in the premium
rates. This is the source of the profit. [1] Page 18 CT5: Q&A Bank Part 2
Solutions IFE: 2013 Examinations The Actuarial Education
Company If the director recalculated his figures with th

Actuarial Education Company IFE: 2013 Examinations and similarly:
( ) 0.45 65:5 1 1 4.02635 0.05 0.04 - = -= + a e [] So the expected
present value of the annuity is: (10,000 4.12100 12,000 0.67032
4.02635 73,597 + = ) ( ) [1] [Total 4] (ii)(a) EPV of ter

aged 32, buys a 12-year temporary assurance with a sum assured of
5,000 payable at the end of year of death. Calculate the annual
premium for this policy. Assume AM92 Select mortality, 4% pa interest
and that premiums are payable annually in advance. Allo

she is still alive at age x + n . [1] II is not correct. The n| a term on the
RHS will make payments even if the life has died. This should be
replaced with the temporary annuity factor | x:n a . [1] CT5: Q&A
Bank Part 1 Solutions Page 5 The Actuarial Edu

years is 10,000 pa, and thereafter it is 12,000 pa. The force of
mortality of this life is 0.03 pa between the ages of 60 and 65, and
0.04 pa between the ages of 65 and 70. Calculate the expected
present value of this annuity assuming a force of interest

take care of your study material to ensure that it is not used or copied
by anybody else. Legal action will be taken if these terms are
infringed. In addition, we may seek to take disciplinary action through
the profession or through your employer. These

deferred annuity is: 20 20 60 60 @0% 60 60 0 [40] [40] 200 1.05 200
= t t t l l v v p dt v a l l [2] We have: 20 20 60 [40] 9,287.2164 1.05
0.3552 9,854.3036 l v l - = = [1] The annuity factor at 0% is the same
as the complete expectation of life 60 e .

profit The present value of the profit to the insurance company is: EPV
Premiums EPV Benefits NPV = - The present value of the premiums is:
2 [60] [60] 1 62 [60] 2 EPV Premiums 3,000 103,735.4 103,061.1
102,040.8 3,000 103,735.4 3,000 2.8127 8,438.10 + +

So: [55]:10 a = 7.959 [1] We see here that the value of the select
annuity is actually lower than the value of the ultimate annuity. We
would normally expect the reverse since the (normally lighter) select
mortality would increase the expected present val

AM92 Ultimate mortality, 4% pa interest, no expenses [3] Question
2.11 A special ten-year increasing endowment assurance policy
provides a sum assured of 10,000 during the first year, which
increases by 1,000 in each subsequent year. The sum payable on
ma

5 10 100 150 50 150 50 m m m + + + + - + - t x xt t x xt t t t x xt
a p dt a a p dt a a p dt [1 ] The first integral is: ( ) 0.04 5 5 0.01 0 0 5
0.01 0.05 0 0.05 0.25 1 100 100 0.01 0.04 100 0.01 0.04 1 1 25 0.01
0.05 11.32683 m - - + - - - - - = = - - -

Development Questions Question 2.1 Calculate the annual premium
payable in advance by a life now aged exactly 32 in respect of a
deferred annuity payable from age 60 for 5 years certain and for life
thereafter. The amount of the annuity is 400 pa, payable