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aduating from school, Ahmet, 30 years old, wants to make a retirement plan for his future with the 50000 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 20 equal annual installments. In the pension plan, the retirement age is set at 70. He wants 300000 TL retirement bonus in the year he retires, 200000 TL death guarantee for life after retirement, and also 25000 TL pension for 10 years at the beginning of each year in his retirement. Interest rate is 6% and according to 1958 CSO Mortality table 1. Write the actuarial equivalence formula 2. Find the annual pre

aduating from school, Ahmet, 30 years old, wants to make a retirement plan for his future with the 50000 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 20 equal annual installments. In the pension plan, the retirement age is set at 70. He wants 300000 TL retirement bonus in the year he retires, 200000 TL death guarantee for life after retirement, and also 25000 TL pension for 10 years at the beginning of each year in his retirement. Interest rate is 6% and according to 1958 CSO Mortality table 1. Write the actuarial equivalence formula 2. Find the annual pre

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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After graduating from school, Ahmet, 30 years old, wants to make a retirement plan for his future with the 50000 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 20 equal annual installments. In the pension plan, the retirement age is set at 70. He wants 300000 TL retirement bonus in the year he retires, 200000 TL death guarantee for life after retirement, and also 25000 TL pension for 10 years at the beginning of each year in his retirement. Interest rate is 6% 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?

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
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
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: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
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