25-year-old Ahmet, after graduating from school, wants to make a retirement plan for his future with the 20000 money his father gave him for graduation. In this retirement planning, he wants to pay the plan's payments in cash, the amount his father gave him, and pay the rest in 5 equal annual installments. In the pension plan, the retirement age is set at 60. He wants a retirement bonus of 200000 TL in the year he retires, a lifelong death guarantee of 200000 TL after retirement, and also a pension of 25000 TL for 10 years at the beginning of each year. Interest rate is 3% and according to 1958 CSO Mortality table

1. Write the actuarial equivalence formula

2. Find the annual premium payments.

3. What is the 5th year end reserve of this pension plan.

4. What is the 45th year end reserve of this pension plan.

5. If Ahmet Bey gives up his current rights 5 years after his retirement and wants a plan where he will be paid a pension for only 10 years at the beginning of each year, how much would the new pension be?
Transcribed Image Text:149 ΚΑΥΝΑKLAR Tablo II (Devamı)- 1958 CSO Mortalite Tablosu (Erkek) e° х 8,698,404 8,610,244 53 8,524,486 54 8,431,654 55 8,331,317 56 8,223,010 57 8,106,161 51 88,160 85,758 92,832 100,337 108,307 116,849 125,970 135,663 145,830 156,592 167,736 179,271 191,174 203,394 215,917 228,749 6,355,865 241,777 254,835 267,241 278,426 287,731 294,766 73 4,731,089 299,289 0.01014 22.80 51 52 53 54 55 56 52 0.00996 22.03 0.01089 21.25 0.01190 20.47 0.01300 19.71 0.01421 18.97 0.01554 18.23 57 58 17.51 58 7,980,191 7,844,528 7,698,698 7,542,106 7,374,370 63 7,195,099 7,003,925 6,800,531 6,584,614 67 0.01700 59 0.01859 16.81 59 60 0.02034 16.12 60 61 0.02224 15.44 61 62 63 64 65 66 67 68 62 0.02431 14.78 0.02657 14.14 64 0.02904 13.51 65 0.03175 12.90 66 0.03474 12.31 0.03804 11.73 6,114,088 5,859,253 70 5,592,012 68 0.04168 11.17 69 0.04561 10.64 69 0.04979 10.12 70 71 5,313,586 72 5,025,855 0.05415 9.63 71 72 73 74 75 76 0.05865 9.15 0.06326 8.69 74 4,431,800 75 4,129,906 301,894 303,011 303,014 301,997 0.06812 8.24 0.07337 7.81 76 3,826,895 3,523,881 3,221,884 79 2,922,055 0.07918 7.39 77 0.08570 6.98 77 78 78 299,829 295,683 0.09306 6.59 0.10119 6.21 79 80 5.85 80 2,626,372 288,848 2,337,524 82 2,058,541 0.10998 81 278,983 265,902 249,858 231,433 0.11935 5.51 81 82 83 84 85 0.12917 5.19 83 1,792,639 1,542,781 1,311,348 211,311 1,100,037 909,929 741,474 594,477 468,174 361,365 272,552 200,072 142,191 97,165 0.13938 4.89 84 0.15001 4.60 85 0.16114 4.32 86 0.17282 86 190,108 168,455 146,997 126,303 106,809 88,813 4.06 87 88 87 0.18513 3.80 88 0.19825 3.55 89 0.21246 3.31 89 90 0.22814 3.06 90 91 0.24577 2.82 91 92 92 72,480 57,881 45,026 34,000 25,378 18,456 12,916 6,415 0.26593 2.58 93 0.28930 2.33 93 94 0.31666 2.07 94 95 0.34992 1.80 95 96 97 96 0.40177 63,165 37,787 19,331 6,415 1.51 97 0.48842 1.18 98 0.66815 0.83 98 99 1.00000 0.50 99 149
Transcribed Image Text:148 ΚΑΥΝΑKLAR Tablo II- 1958 CSO Mortalite Tablosu (Erkek) 4x *p O 10,000,000 9,929,200 2 9,911,725 9,896,659 70,800 17,475 15,066 14,449 0.00708 68.30 1 0.00176 67.78 1 0.00152 66.90 3 0.00146 66.00 3 4 9,882,210 0.00140 65.10 4 13,835 13,322 12,812 12,401 12,091 11,879 11,865 12,047 12,325 12,896 13,562 14,225 14,983 15,737 16,390 16,846 17,300 17,655 17,912 18,167 18,324 18,481 18,732 18,981 19,324 19,760 20,193 20,718 21,239 21,850 22,551 9,868,375 9,855,053 9,842,241 8 0.00135 64.19 0.00130 63.27 6 7 0.00126 62.35 7 9,829,840 9,817,749 10 9,805,870 9,794,005 12 9,781,958 13 9,769,633 14 9,756,737 15 9,743,175 16 9,728,950 17 9,713,967 18 9,698,230 9,681,840 9,664,994 9,647,694 22 9,630,039 23 9,612,127 24 9,593,960 25 9,575,636 26 9,557,155 27 9,538,423 28 9,519,442 29 9,500,118 0.00123 61.43 9. 0.00121 60.51 0.00121 59.58 10 11 0.00123 58.65 11 0.00126 57.72 12 0.00132 56.80 13 0.00139 55.87 14 0.00146 54.95 15 0.00154 54.03 16 0.00162 53.11 17 0.00169 52.20 18 19 0.00174 51.28 19 20 0.00179 50.37 20 21 0.00183 49.46 21 0.00186 48.55 22 0.00189 47.64 23 0.00191 46.73 24 0.00193 45.82 25 0.00196 44.91 26 0.00199 43.99 27 0.00203 43.08 28 0.00208 42.17 29 30 0.00213 30 9,480,358 31 9,460,165 32 9,439,447 33 9,418,208 34 9,396,358 35 9,373,807 36 9,350,279 37 9,325,594 9,299,482 39 41.25 0.00219 40.34 31 0.00225 39.43 32 0.00232 38.51 33 0.00240 37.60 34 0.00251 36.69 35 23,528 24,685 0.00264 35.78 36 0.00280 34.88 37 26,112 27,991 30,132 32,622 35,362 38,253 41,382 44,741 48,412 52,473 56,910 61,794 38 0.00301 33.97 38 39 9,271,491 40 9,241,359 0.00325 33.07 0.00353 32.18 40 41 41 9,208,737 42 9,173,375 43 9,135,122 44 9,093,740 45 9,048,999 46 9,000,587 47 8,948,114 48 8,891,204 8,829,410 50 8,762,306 0.00384 31.29 0.00417 30.41 42 0.00453 29.54 43 0.00492 28.67 44 0.00535 27.81 45 0.00583 26.96 46 0.00636 26.11 47 0.00695 25.27 48 49 67,104 0.00760 24.45 49 63,902 0.00729 23.63 50 148

Name: 25-year-old Ahmet, after graduating from school, wants to make a retir
Uploaded: 2024-03-05T11:52:21.000Z
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Description: 25-year-old Ahmet, after graduating from school, wants to make a retirement plan for his future with the 20000 money his father gave him for graduation. In this retirement planning, he wants to pay the plan's payments in cash, the amount his father g

Question

25-year-old Ahmet, after graduating from school, wants to make a retirement plan for his future with the 20000 money his father gave him for graduation. In this retirement planning, he wants to pay the plan's payments in cash, the amount his father gave him, and pay the rest in 5 equal annual installments. In the pension plan, the retirement age is set at 60. He wants a retirement bonus of 200000 TL in the year he retires, a lifelong death guarantee of 200000 TL after retirement, and also a pension of 25000 TL for 10 years at the beginning of each year. Interest rate is 3% and according to 1958 CSO Mortality table

1. Write the actuarial equivalence formula

2. Find the annual premium payments.

3. What is the 5th year end reserve of this pension plan.

4. What is the 45th year end reserve of this pension plan.

5. If Ahmet Bey gives up his current rights 5 years after his retirement and wants a plan where he will be paid a pension for only 10 years at the beginning of each year, how much would the new pension be?

149
ΚΑΥΝΑKLAR
Tablo II (Devamı)- 1958 CSO Mortalite Tablosu (Erkek)
e°
х
8,698,404
8,610,244
53 8,524,486
54 8,431,654
55 8,331,317
56 8,223,010
57 8,106,161
51
88,160
85,758
92,832
100,337
108,307
116,849
125,970
135,663
145,830
156,592
167,736
179,271
191,174
203,394
215,917
228,749
6,355,865 241,777
254,835
267,241
278,426
287,731
294,766
73 4,731,089 299,289
0.01014
22.80
51
52
53
54
55
56
52
0.00996
22.03
0.01089
21.25
0.01190
20.47
0.01300
19.71
0.01421
18.97
0.01554
18.23
57
58
17.51
58
7,980,191
7,844,528
7,698,698
7,542,106
7,374,370
63 7,195,099
7,003,925
6,800,531
6,584,614
67
0.01700
59
0.01859
16.81
59
60
0.02034
16.12
60
61
0.02224
15.44
61
62
63
64
65
66
67
68
62
0.02431
14.78
0.02657
14.14
64
0.02904
13.51
65
0.03175
12.90
66
0.03474
12.31
0.03804
11.73
6,114,088
5,859,253
70 5,592,012
68
0.04168
11.17
69
0.04561
10.64
69
0.04979
10.12
70
71
5,313,586
72 5,025,855
0.05415
9.63
71
72
73
74
75
76
0.05865
9.15
0.06326
8.69
74 4,431,800
75 4,129,906
301,894
303,011
303,014
301,997
0.06812
8.24
0.07337
7.81
76
3,826,895
3,523,881
3,221,884
79 2,922,055
0.07918
7.39
77
0.08570
6.98
77
78
78
299,829
295,683
0.09306
6.59
0.10119
6.21
79
80
5.85
80
2,626,372 288,848
2,337,524
82 2,058,541
0.10998
81
278,983
265,902
249,858
231,433
0.11935
5.51
81
82
83
84
85
0.12917
5.19
83
1,792,639
1,542,781
1,311,348 211,311
1,100,037
909,929
741,474
594,477
468,174
361,365
272,552
200,072
142,191
97,165
0.13938
4.89
84
0.15001
4.60
85
0.16114
4.32
86
0.17282
86
190,108
168,455
146,997
126,303
106,809
88,813
4.06
87
88
87
0.18513
3.80
88
0.19825
3.55
89
0.21246
3.31
89
90
0.22814
3.06
90
91
0.24577
2.82
91
92
92
72,480
57,881
45,026
34,000
25,378
18,456
12,916
6,415
0.26593
2.58
93
0.28930
2.33
93
94
0.31666
2.07
94
95
0.34992
1.80
95
96
97
96
0.40177
63,165
37,787
19,331
6,415
1.51
97
0.48842
1.18
98
0.66815
0.83
98
99
1.00000
0.50
99
149

148
ΚΑΥΝΑKLAR
Tablo II- 1958 CSO Mortalite Tablosu (Erkek)
4x
*p
O 10,000,000
9,929,200
2 9,911,725
9,896,659
70,800
17,475
15,066
14,449
0.00708
68.30
1
0.00176
67.78
1
0.00152
66.90
3
0.00146
66.00
3
4
9,882,210
0.00140
65.10
4
13,835
13,322
12,812
12,401
12,091
11,879
11,865
12,047
12,325
12,896
13,562
14,225
14,983
15,737
16,390
16,846
17,300
17,655
17,912
18,167
18,324
18,481
18,732
18,981
19,324
19,760
20,193
20,718
21,239
21,850
22,551
9,868,375
9,855,053
9,842,241
8
0.00135
64.19
0.00130
63.27
6
7
0.00126
62.35
7
9,829,840
9,817,749
10 9,805,870
9,794,005
12 9,781,958
13 9,769,633
14 9,756,737
15 9,743,175
16 9,728,950
17 9,713,967
18 9,698,230
9,681,840
9,664,994
9,647,694
22 9,630,039
23 9,612,127
24 9,593,960
25 9,575,636
26 9,557,155
27 9,538,423
28 9,519,442
29 9,500,118
0.00123
61.43
9.
0.00121
60.51
0.00121
59.58
10
11
0.00123
58.65
11
0.00126
57.72
12
0.00132
56.80
13
0.00139
55.87
14
0.00146
54.95
15
0.00154
54.03
16
0.00162
53.11
17
0.00169
52.20
18
19
0.00174
51.28
19
20
0.00179
50.37
20
21
0.00183
49.46
21
0.00186
48.55
22
0.00189
47.64
23
0.00191
46.73
24
0.00193
45.82
25
0.00196
44.91
26
0.00199
43.99
27
0.00203
43.08
28
0.00208
42.17
29
30
0.00213
30
9,480,358
31 9,460,165
32 9,439,447
33 9,418,208
34 9,396,358
35 9,373,807
36 9,350,279
37 9,325,594
9,299,482
39
41.25
0.00219
40.34
31
0.00225
39.43
32
0.00232
38.51
33
0.00240
37.60
34
0.00251
36.69
35
23,528
24,685
0.00264
35.78
36
0.00280
34.88
37
26,112
27,991
30,132
32,622
35,362
38,253
41,382
44,741
48,412
52,473
56,910
61,794
38
0.00301
33.97
38
39
9,271,491
40 9,241,359
0.00325
33.07
0.00353
32.18
40
41
41
9,208,737
42 9,173,375
43 9,135,122
44 9,093,740
45 9,048,999
46 9,000,587
47 8,948,114
48 8,891,204
8,829,410
50 8,762,306
0.00384
31.29
0.00417
30.41
42
0.00453
29.54
43
0.00492
28.67
44
0.00535
27.81
45
0.00583
26.96
46
0.00636
26.11
47
0.00695
25.27
48
49
67,104
0.00760
24.45
49
63,902
0.00729
23.63
50
148

Accepted Answer

25-year-old Ahmet, after graduating from school, wants to make a retirement plan for his future with…