On her 45th birthday, Lisa Martin takes out a 20-year endowment policy with a £50,000 death benefit payable at the end of the year of death and a £30,000 survival benefit. The premium is payable annually in arrears. Assume an effective annual interest rate of 4% and the mortality given by table AMC00 ultimate values. (a) Calculate the expected present value of the survival benefit. (b) Calculate the expected present value of the death benefit. (c) What is the annual premium for the endowment policy?
On her 45th birthday, Lisa Martin takes out a 20-year endowment policy with a £50,000 death benefit payable at the end of the year of death and a £30,000 survival benefit. The premium is payable annually in arrears. Assume an effective annual interest rate of 4% and the mortality given by table AMC00 ultimate values. (a) Calculate the expected present value of the survival benefit. (b) Calculate the expected present value of the death benefit. (c) What is the annual premium for the endowment policy?
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
Related questions
Question
Transcribed Image Text:On her 45th birthday, Lisa Martin takes out a 20-year endowment policy with a
£50,000 death benefit payable at the end of the year of death and a £30,000 survival
benefit. The premium is payable annually in arrears. Assume an effective annual
interest rate of 4% and the mortality given by table AMC00 ultimate values.
(a) Calculate the expected present value of the survival benefit.
(b) Calculate the expected present value of the death benefit.
(c) What is the annual premium for the endowment policy?
![AMC00 Male Life Table
Age x Age x
59
60
61
62
63
64
65
66
67
68
69
Age x
17
[x-1]+1
[x]
9997.5094
lx
10000.0000 17
9995.4200 18
9990.8321 19
9986.2163 20
9981.5827
9976.9213
21
22
9972.2222
23
18 9992.9305 9994.6901
19 9988.3337 9990.1025
20 9983.6991 9985.4871
21 9979.0567 9980.8438
22 9974.3666 9976.1827
23 9969.6487 9971.4740
9964.8832 9966.7276 9967.4854
9960.0701 9961.9336 9962.7010
9955.1996 9957.0921 9957.8691 26
9950.2618 9952.1832 9952.9698 27
9945.2469 9947.1972 9947.9933 28
9940.1847 9942.1340 9942.9398
30 9935.0655 9936.9939 9937.7794
24
24
25
25
26
27
28
29
29
30
31
32
9929.8794 9931.7671 9932.5024 31
9924.5767 9926.4238 9927.0892 32
9919.1182 9920.9344 9921.5201
33
33
34
34
35
9913.4841 9915.2596 9915.7755
9907.6152 9909.3799 9909.8162 35
9901.4922 9903.2460 9903.6126
36
36
37
38
9895.0760 9896.8385 9897.1357 37
9888.3275 9890.1087 9890.3363 38
39 9881.1880 9882.9977 9883.1559
40 9873.5893 9875.4570
39
9875.5558 40
9867.4578 41
41 9865.4534 9867.4085
42 9856.7223 9858.7745 9858.7942
44
48
49
50
43 9847.3090 9849.4875 9849.4875 43
44 9837.1169 9839.4312 9839.4312
45 9826.0499 9828.5291 9828.5291 45
46 9813.9735 9816.6562 9816.6562 46
47 9800.7439 9803.6786 9803.6786 47
9786.2090 9789.4437 9789.4437 48
9770.1885 9773.7708 9773.7708 49
9752.4550 9756.4712 9756.4712 50
9732.8031 9737.3192 9737.3192 51
9710.9228 9716.0627 9716.0627 52
9686.5083 9692.4138 9692.4332 53
54 9659.2100 9666.0213 9666.1182 54
55 9628.6170 9636.5205 9636.7719 55
56 9594.3554 9603.4960 9604.0069 56
57 9555.9547 9566.5317 9567.3964 57
58 9512.9284 9525.1558 9526.4767 58
51
52
53
22
42
[x-1]+1
Age x
1 [x]
9464.7096 9478.8531 9480.7305 59
9410.6849 9427.0212 9429.5820 60
9350.1805 9369.0144 9372.4010 61
9282.4873 9304.1589 | 9308.5187 62
9206.8320 9231.7028 9237.1968 63
9122.3956 9150.8360 9157.6369 64
9028.3257 9060.7100 9069.0001 65
8923.7129 8960.4327 8970.3747 66
8807.6361 8849.0571 8860.8106 67
8679.1539 8725.6105 8739.3111
8537.3365 8589.1250 8604.8568
8381.2654 8438.6022 8456.4058
70
77
71 8210.1056 8273.0800 8292.9181
8023.0608 8091.6666 8113.3848
7819.4936 7893.5124 7916.8461
7598.8879 7677.9138 7702.4263
7360.9680 7444.3113 7469.3894
7105.6585 7192.3651 7217.1705
6833.2053 6921.9772 6945.4296
6543.2750 6633.3614 6654.1244 78
6234.6920 6326.2215 6343.5631 79
5905.8869 6000.3050 6014.4463 80
5557.1270 5655.4241 5667.9541 81
5191.0860 5293.5691 5305.7888 82
4811.5773 4917.5469 4930.2080 83
4422.4381 4531.0383 4544.0494 84
4027.2597 4137.4915 4150.7347 85
3630.1730 3740.8772 3754.2191 86
3235.7358 3345.6473 3358.9374 87
2848.8406 2956.5986 2969.6769 88
89 2474.5254 2578.7306 2591.4291 89
90 2117.7709 2217.0436 2229.1940 90
91
81
82
83
84
85
86
87
88
1876.3069 1887.7528 91
92
93
94
95
96
97
98
99
100
72
73
74
75
76
77
78
8 79 80
ESBRF NR NERE
614.5164
457.2229
68
69
70
71
72
73
74
75
76
1571.4202 92
1283.8047 93
1027.5920 94
804.3661 95
96
97
330.5502 98
231.6268 99
156.9026 100](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb5bc28c8-e2da-4655-bd50-d87af98278d3%2F0e4c6331-17ac-4a6b-af5b-885a47a75c6f%2Fz5oiut_processed.png&w=3840&q=75)
Transcribed Image Text:AMC00 Male Life Table
Age x Age x
59
60
61
62
63
64
65
66
67
68
69
Age x
17
[x-1]+1
[x]
9997.5094
lx
10000.0000 17
9995.4200 18
9990.8321 19
9986.2163 20
9981.5827
9976.9213
21
22
9972.2222
23
18 9992.9305 9994.6901
19 9988.3337 9990.1025
20 9983.6991 9985.4871
21 9979.0567 9980.8438
22 9974.3666 9976.1827
23 9969.6487 9971.4740
9964.8832 9966.7276 9967.4854
9960.0701 9961.9336 9962.7010
9955.1996 9957.0921 9957.8691 26
9950.2618 9952.1832 9952.9698 27
9945.2469 9947.1972 9947.9933 28
9940.1847 9942.1340 9942.9398
30 9935.0655 9936.9939 9937.7794
24
24
25
25
26
27
28
29
29
30
31
32
9929.8794 9931.7671 9932.5024 31
9924.5767 9926.4238 9927.0892 32
9919.1182 9920.9344 9921.5201
33
33
34
34
35
9913.4841 9915.2596 9915.7755
9907.6152 9909.3799 9909.8162 35
9901.4922 9903.2460 9903.6126
36
36
37
38
9895.0760 9896.8385 9897.1357 37
9888.3275 9890.1087 9890.3363 38
39 9881.1880 9882.9977 9883.1559
40 9873.5893 9875.4570
39
9875.5558 40
9867.4578 41
41 9865.4534 9867.4085
42 9856.7223 9858.7745 9858.7942
44
48
49
50
43 9847.3090 9849.4875 9849.4875 43
44 9837.1169 9839.4312 9839.4312
45 9826.0499 9828.5291 9828.5291 45
46 9813.9735 9816.6562 9816.6562 46
47 9800.7439 9803.6786 9803.6786 47
9786.2090 9789.4437 9789.4437 48
9770.1885 9773.7708 9773.7708 49
9752.4550 9756.4712 9756.4712 50
9732.8031 9737.3192 9737.3192 51
9710.9228 9716.0627 9716.0627 52
9686.5083 9692.4138 9692.4332 53
54 9659.2100 9666.0213 9666.1182 54
55 9628.6170 9636.5205 9636.7719 55
56 9594.3554 9603.4960 9604.0069 56
57 9555.9547 9566.5317 9567.3964 57
58 9512.9284 9525.1558 9526.4767 58
51
52
53
22
42
[x-1]+1
Age x
1 [x]
9464.7096 9478.8531 9480.7305 59
9410.6849 9427.0212 9429.5820 60
9350.1805 9369.0144 9372.4010 61
9282.4873 9304.1589 | 9308.5187 62
9206.8320 9231.7028 9237.1968 63
9122.3956 9150.8360 9157.6369 64
9028.3257 9060.7100 9069.0001 65
8923.7129 8960.4327 8970.3747 66
8807.6361 8849.0571 8860.8106 67
8679.1539 8725.6105 8739.3111
8537.3365 8589.1250 8604.8568
8381.2654 8438.6022 8456.4058
70
77
71 8210.1056 8273.0800 8292.9181
8023.0608 8091.6666 8113.3848
7819.4936 7893.5124 7916.8461
7598.8879 7677.9138 7702.4263
7360.9680 7444.3113 7469.3894
7105.6585 7192.3651 7217.1705
6833.2053 6921.9772 6945.4296
6543.2750 6633.3614 6654.1244 78
6234.6920 6326.2215 6343.5631 79
5905.8869 6000.3050 6014.4463 80
5557.1270 5655.4241 5667.9541 81
5191.0860 5293.5691 5305.7888 82
4811.5773 4917.5469 4930.2080 83
4422.4381 4531.0383 4544.0494 84
4027.2597 4137.4915 4150.7347 85
3630.1730 3740.8772 3754.2191 86
3235.7358 3345.6473 3358.9374 87
2848.8406 2956.5986 2969.6769 88
89 2474.5254 2578.7306 2591.4291 89
90 2117.7709 2217.0436 2229.1940 90
91
81
82
83
84
85
86
87
88
1876.3069 1887.7528 91
92
93
94
95
96
97
98
99
100
72
73
74
75
76
77
78
8 79 80
ESBRF NR NERE
614.5164
457.2229
68
69
70
71
72
73
74
75
76
1571.4202 92
1283.8047 93
1027.5920 94
804.3661 95
96
97
330.5502 98
231.6268 99
156.9026 100
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