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Calculate the minimum premium for whole life insurance policy of one million yen, following the instructions, using the following assumptions: Discount rate of 3% Nobody
Calculate the minimum premium for whole life insurance policy of one million yen, following the instructions, using the following assumptions: Discount rate of 3% Nobody will live to 106 No business expenses/profits for insurer Age Death rate 20 0.00020 21 0.00021 22 0.00022 23 0.00022 24 0.00022 25 0.00022 26 0.00023 27 0.00024 28 0.00025 29 0.00025 30 0.00027 31 0.00029 32 0.00031 33 0.00034 34 0.00037 35 0.00040 36 0.00042 37 0.00044 38 0.00047 39 0.00051 40 0.00057 41 0.00062 42 0.00068 43 0.00074 44 0.00081 45 0.00089 46 0.00099 47 0.00110 48 0.00121 49 0.00133 50 0.00243 51 0.00269 52 0.00298 53 0.00327 54 0.00359 55 0.00395 56 0.00434 57 0.00478 58 0.00530 59 0.00585 60 0.00644 61 0.00709 62 0.00777 63 0.00852 64 0.00936 65 0.01030 66 0.01138 67 0.01259 68 0.01395 69 0.01546 70 0.01694 71 0.01844 72 0.02010 73 0.02204 74 0.02432 75 0.02684 76 0.02953 77 0.03229 78 0.03562 79 0.03984 80 0.04493 81 0.05072 82 0.05711 83 0.06419 84 0.07230 85 0.08179 86 0.09269 87 0.10497 88 0.11835 89 0.13221 90 0.14537 91 0.16073 92 0.17747 93 0.19568 94 0.21544 95 0.23682 96 0.25989 97 0.28471 98 0.31130 99 0.33969 100 0.36985 101 0.40176 102 0.43531 103 0.47038 104 0.50680 105 1.00000
3. The next step is to calculate the discount factor for each age, and work out the present values of premium at each age. For example, the discount factor is (two decimal points) at age 60, and the present value of the premium at that age is yen (no 1,000 separators in the box please), 4. The final step is to factor in the survival rate. For example, since only people will be surviving at age 105, the present value of premium that need to be prepaid at the beginning is yen, which far smaller than the premium calculated in the second step. (no 1,000 separators in the boxes please)
5. The (minimum) premium for a whole life insurance policy would thus be yen. (no 1,000 separators in the box please)
Discount rate of 3%
Nobody will live to 106
No business expenses/profits for insurer
Age | Death rate |
20 | 0.00020 |
21 | 0.00021 |
22 | 0.00022 |
23 | 0.00022 |
24 | 0.00022 |
25 | 0.00022 |
26 | 0.00023 |
27 | 0.00024 |
28 | 0.00025 |
29 | 0.00025 |
30 | 0.00027 |
31 | 0.00029 |
32 | 0.00031 |
33 | 0.00034 |
34 | 0.00037 |
35 | 0.00040 |
36 | 0.00042 |
37 | 0.00044 |
38 | 0.00047 |
39 | 0.00051 |
40 | 0.00057 |
41 | 0.00062 |
42 | 0.00068 |
43 | 0.00074 |
44 | 0.00081 |
45 | 0.00089 |
46 | 0.00099 |
47 | 0.00110 |
48 | 0.00121 |
49 | 0.00133 |
50 | 0.00243 |
51 | 0.00269 |
52 | 0.00298 |
53 | 0.00327 |
54 | 0.00359 |
55 | 0.00395 |
56 | 0.00434 |
57 | 0.00478 |
58 | 0.00530 |
59 | 0.00585 |
60 | 0.00644 |
61 | 0.00709 |
62 | 0.00777 |
63 | 0.00852 |
64 | 0.00936 |
65 | 0.01030 |
66 | 0.01138 |
67 | 0.01259 |
68 | 0.01395 |
69 | 0.01546 |
70 | 0.01694 |
71 | 0.01844 |
72 | 0.02010 |
73 | 0.02204 |
74 | 0.02432 |
75 | 0.02684 |
76 | 0.02953 |
77 | 0.03229 |
78 | 0.03562 |
79 | 0.03984 |
80 | 0.04493 |
81 | 0.05072 |
82 | 0.05711 |
83 | 0.06419 |
84 | 0.07230 |
85 | 0.08179 |
86 | 0.09269 |
87 | 0.10497 |
88 | 0.11835 |
89 | 0.13221 |
90 | 0.14537 |
91 | 0.16073 |
92 | 0.17747 |
93 | 0.19568 |
94 | 0.21544 |
95 | 0.23682 |
96 | 0.25989 |
97 | 0.28471 |
98 | 0.31130 |
99 | 0.33969 |
100 | 0.36985 |
101 | 0.40176 |
102 | 0.43531 |
103 | 0.47038 |
104 | 0.50680 |
105 | 1.00000 |
3. The next step is to calculate the discount factor for each age, and work out the present values of premium at each age. For example, the discount factor is (two decimal points) at age 60, and the present value of the premium at that age is yen (no 1,000 separators in the box please),
4. The final step is to factor in the survival rate. For example, since only people will be surviving at age 105, the present value of premium that need to be prepaid at the beginning is yen, which far smaller than the premium calculated in the second step. (no 1,000 separators in the boxes please)
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