Actuarial Science
SPRING 2016 ACTUARIAL METHOD I PROF. RAMANUJAM
Homework Set #2
1. You are given:
i) qx = 0.2
ii) qx+1 = 0.4
iii) qx+2 = 0.6
iv) qx+3 = 0.8
v) qx+4 = 1.0
vi) ?? = 0.06
Calculate a) Ax; b) ????:3¯|
1 ; c) ????:3¯|
1 ; d)2Ax
2. You are given:
i) qx = 0.2
ii) 1|???? = 0.2
iii) 2|???? = 3|???? = 4|???? = 0.2
i) ?? = 0.06
Calculate a) Ax; b) ????:3¯|
1 ; c) ????:3¯|
1 ; d)2Ax
3. In problem #1, calculate ??¯?? and 2??¯?? under UDD
4. In problem #2, calculate ??¯
??:3¯| and 2??¯?? under UDD
5. You are given:
i) ??50:¯2¯¯0¯¯| = 0.42247
ii) ??50:¯2¯¯0¯¯|
1 = 0.14996
iii) ??50 = 0.31266
Calculate ??70
6. You are given:
i) ???? = 0.25
ii) ????+20 = 0.4
iii) ????:¯2¯¯0¯¯| = 0.55
iv) ?? = 0.03
Calculate 10000 ??¯
??:¯2¯¯0¯¯| under a) UDD and b) claims acceleration method
7. You are given:
i) (IA)50 = 4.99675
ii) ??50:1¯|
1 = 0.00558
iii) ??51 = 0.24905
iv) ?? = 0.06
Calculate (IA)51
8. You are given:
i) X denotes the present value of the random variable for n-year endowment
and Y denotes the present value of the random variable for n-year term
insurance(X and Y are both continuous).
ii) Var(X) = 0.0052
iii) vn = 0.3
iv) npx = 0.8
v) E(Y) = 0.04
Calculate Var(Y)
9. ??1 = {
?????? , ???? = ??
0, ???? > ??
and ??2 = {
0, ???? = ??
????, ???? > ??
Calculate Cov(Z1, Z2)
10. You are given:
x lx Ax
35 100000.00 0.151375
36 99737.15 0.158245
37 99455.91 0.165386
38 99154.72 0.172804
39 98831.91 0.180505
40 98485.68 0.188492
?? = 6%
Calculate a) 5E35; b) ??35:5¯|
1 ; c) 5|??35; d) ??¯
35:5¯| under UDD

Actuarial Science
SPRING 2016 ACTUARIAL METHOD I PROF. RAMANUJAM
Homework Set #2
1. You are given:
i) qx = 0.2
ii) qx+1 = 0.4
iii) qx+2 = 0.6
iv) qx+3 = 0.8
v) qx+4 = 1.0
vi) ?? = 0.06
Calculate a) Ax; b) ????:3¯|
1 ; c) ????:3¯|
1 ; d)2Ax
2. You are given:
i) qx = 0.2
ii) 1|???? = 0.2
iii) 2|???? = 3|???? = 4|???? = 0.2
i) ?? = 0.06
Calculate a) Ax; b) ????:3¯|
1 ; c) ????:3¯|
1 ; d)2Ax
3. In problem #1, calculate ??¯?? and 2??¯?? under UDD
4. In problem #2, calculate ??¯
??:3¯| and 2??¯?? under UDD
5. You are given:
i) ??50:¯2¯¯0¯¯| = 0.42247
ii) ??50:¯2¯¯0¯¯|
1 = 0.14996
iii) ??50 = 0.31266
Calculate ??70
6. You are given:
i) ???? = 0.25
ii) ????+20 = 0.4
iii) ????:¯2¯¯0¯¯| = 0.55
iv) ?? = 0.03
Calculate 10000 ??¯
??:¯2¯¯0¯¯| under a) UDD and b) claims acceleration method
7. You are given:
i) (IA)50 = 4.99675
ii) ??50:1¯|
1 = 0.00558
iii) ??51 = 0.24905
iv) ?? = 0.06
Calculate (IA)51
8. You are given:
i) X denotes the present value of the random variable for n-year endowment
and Y denotes the present value of the random variable for n-year term
insurance(X and Y are both continuous).
ii) Var(X) = 0.0052
iii) vn = 0.3
iv) npx = 0.8
v) E(Y) = 0.04
Calculate Var(Y)
9. ??1 = {
?????? , ???? = ??
0, ???? > ??
and ??2 = {
0, ???? = ??
????, ???? > ??
Calculate Cov(Z1, Z2)
10. You are given:
x lx Ax
35 100000.00 0.151375
36 99737.15 0.158245
37 99455.91 0.165386
38 99154.72 0.172804
39 98831.91 0.180505
40 98485.68 0.188492
?? = 6%
Calculate a) 5E35; b) ??35:5¯|
1 ; c) 5|??35; d) ??¯
35:5¯| under UDD

Actuarial Science
SPRING 2016 ACTUARIAL METHOD I PROF. RAMANUJAM
Homework Set #2
1. You are given:
i) qx = 0.2
ii) qx+1 = 0.4
iii) qx+2 = 0.6
iv) qx+3 = 0.8
v) qx+4 = 1.0
vi) ?? = 0.06
Calculate a) Ax; b) ????:3¯|
1 ; c) ????:3¯|
1 ; d)2Ax
2. You are given:
i) qx = 0.2
ii) 1|???? = 0.2
iii) 2|???? = 3|???? = 4|???? = 0.2
i) ?? = 0.06
Calculate a) Ax; b) ????:3¯|
1 ; c) ????:3¯|
1 ; d)2Ax
3. In problem #1, calculate ??¯?? and 2??¯?? under UDD
4. In problem #2, calculate ??¯
??:3¯| and 2??¯?? under UDD
5. You are given:
i) ??50:¯2¯¯0¯¯| = 0.42247
ii) ??50:¯2¯¯0¯¯|
1 = 0.14996
iii) ??50 = 0.31266
Calculate ??70
6. You are given:
i) ???? = 0.25
ii) ????+20 = 0.4
iii) ????:¯2¯¯0¯¯| = 0.55
iv) ?? = 0.03
Calculate 10000 ??¯
??:¯2¯¯0¯¯| under a) UDD and b) claims acceleration method
7. You are given:
i) (IA)50 = 4.99675
ii) ??50:1¯|
1 = 0.00558
iii) ??51 = 0.24905
iv) ?? = 0.06
Calculate (IA)51
8. You are given:
i) X denotes the present value of the random variable for n-year endowment
and Y denotes the present value of the random variable for n-year term
insurance(X and Y are both continuous).
ii) Var(X) = 0.0052
iii) vn = 0.3
iv) npx = 0.8
v) E(Y) = 0.04
Calculate Var(Y)
9. ??1 = {
?????? , ???? = ??
0, ???? > ??
and ??2 = {
0, ???? = ??
????, ???? > ??
Calculate Cov(Z1, Z2)
10. You are given:
x lx Ax
35 100000.00 0.151375
36 99737.15 0.158245
37 99455.91 0.165386
38 99154.72 0.172804
39 98831.91 0.180505
40 98485.68 0.188492
?? = 6%
Calculate a) 5E35; b) ??35:5¯|
1 ; c) 5|??35; d) ??¯
35:5¯| under UDD