Resenja primera zadataka za drugi kolokvijum iz FAM.pdf

Univerzitet Singidunum
Poslovni fakultet Beograd – 3.godina
Rešenja primera zadataka za 2. kolokvijum iz Finansijske i aktuarske matematike
1.
a)
b)
p
l
63469
69517
50+
5
5 50
= = =
l50
0,91
l50+
15 46754
15
q50
= 1−15
p50
= 1−
= 1−
= 0,33
l 69517
50
c)
15
q50
−5
q50
= 0,33 − (1 − 0,91) = 0,24
2.
l
l
l
n ≈ 28
3.
40+
n
40
40+
n
a
40
=
=
1
2
= 0.5*78653 = 39326, => l
N
D
40
40
=
M = 50000* a
263643,62
l 6382,56
40
= 804647,20
69
< l
40+
n
< l
68
4.
a) b)
N
45
− N
45+
15
a45
=
15
D
15
45
M = 15000*
a45
= 157627,20
15
a'
N
45+
1 45+
15+
1
45
=
Dx
M = 15000 *
− N
15
a'
45

5.
6.
7.
8.
9.
38104,06
100000*
6382,56
l
6242,42
40
40
40
40
=
=
=
=
A
M
D
M
A
10.
11.
118072,60
)
100
*10
20000*(
5,3669
40
15
40
15
40
15
40
40
15
=
+
=
=
= +
a
a
M
D
N
a
21172,43
)
(
10000 *
N
-
N
N
)
(
35
10
10
35
35
35
35
10
=
=
=
+
a
P
P
a
P
20462,74
)
(
25000 *
N
-
N
N
N
)
(
40
15
10
9
9
40
40
15
10
40
10
40
40
15
10
9
=
=
−
=
+
+
+
+
a
P
P
a
P
28774,56
*
100000 40
10
40
10
40
40
10
=
=
= +
A
M
D
M
A
23537,2
*
100000 50
15
50
15
50
50
50
15
=
=
−
= +
A
M
D
M
M
A
12132,51
)
(
10000 *
N
-
N
N
)
(
35
10
9
9
35
35
10
35
35
10
9
=
=
=
+
+
a
P
P
a
P

12.
13.
41754,32
*
100000 45
15
45
15
45
45
15
=
=
= +
E
M
D
D
E
14.
15.
3577,60
)
(
100000*
0,035776
)
(
50
50
50
50
=
=
=
=
A
P
P
N
M
A
P
16.
17.
18.
21315,37
*
100000 45
20
15
45
20
15
45
15
45
45
20
15
=
=
−
= +
+
+
A
M
D
M
M
A
52598,90
*
100000 20
45,
45
20
45
20
45
45
45,20
=
=
+
−
= +
+
A
M
D
D
M
M
A
4738,21
)
(
100000 *
M
)
(
50
15
15
50
50
50
50
15
=
=
−
=
+
A
P
P
N
N
A
P
1395,92
)
(
100000 *
)
(
35
20
/
15
15
35
35
20
35
35
35
20
/
15
=
=
−
−
=
+
+
A
P
P
N
N
M
M
A
P
7487,69
)
(
100000 *
)
(
45,15
10
10
45
45
15
45
15
45
45
45,15
10
=
=
−
+
−
=
+
+
+
A
P
P
N
N
D
M
M
A
P

19. Pretpostavimo da se premija plaća 25 puta.
D40+
P = 100000* P(
25/ 25
E40
) = 100000*
N
40
− N
D40+
25
a
40
=
25
E40
= = 0,44807
D
Π
25
40
=
40
⎡
= ⎢P
⎣
40
20.
M
50
P
50
= 100000* = 3577,60
N50
N50
a = 13,47032
D
Π
50
=
50
50
⎡
= ⎢P
⎣
50
40
23.
l40+
15
l35+
15
15
p
40'35
= * (1 − ) = 0,127656
l l
40
35
40+
25
100000*35 100000*25⎤
1000
+
+ ⎥ *
1000* a40
1000 ⎦ 1000 − 5
100000*5 100000*2⎤
1000
+ + ⎥ *
1000* a50
1000 ⎦ 1000 −1
21.
l40+
20
l35+
20
20
q4035
= 1−
* = 0,453054
l l
40
22.
l40+
15
l35+
15
15
p4035
= * = 0,679293
l l
40
35
35
1578,88