1 Life Insurance (50') The following table present the cash flow arrangement of a life insurance (including critical illness) policy. Use the information in the table to answer the following questions. Assume all premiums are paid at the beginning of each year, and all payments (death benefit and surrender value) are paid at the end of each year. 0 0 0 1 2 3 4 5 6 O 978 D 9 12 PRUmyhealth lifelong crisis protector IMPORTANT: THIS IS A SUMMARY ILLUSTRATION OF THE BENEFITS OF YOUR POLICY AND IN NO WAY AFFECTS THE TERMS AND CONDITIONS STATED IN THE POLICY DOCUMENT. Name Mr. Chan Tai Man Age Next Birthday (ANB) 45 Sex: Male (Non-smoker) Initial Sum Assured : US$ 128,000 Initial Annual Premium : US$ 4,879.36 Benefit Term : Whole Life Premium Term : 20 years Basic Plan - Hlustration Summary (Currency: USS) Surrender Benefit Major Disease Benefit/ Death Benefit Guaranteed Sum Assured Cash Value of PRUmyhealth Face Value of Guaranteed Non-Guaranteed lifelong crisis Free 10-year Non-Guaranteed End of Cash Value Terminal Bonus Total protector crisis cover Terminal Bonus Total Total Policy Year (A) (B) (A)+(B) (C) (D) (E) (C)+(D)+(E) Premiums 0 0 128,000 44,800 172.600 4,879 0 128,000 44,000 0 172.800 9.750 368 0 368 128.000 44.800 172.800 14,638 976 128.000 44,800 172.800 19,517 1,830 383 2.213 128,000 44,800 1.276 174,076 24,397 2.928 743 3,671 128.000 44.800 1 508 174.305 29.276 7 4,269 1.262 5,531 128.000 44.800 1.748 174,548 34,156 8 5.855 2.152 8,007 128.000 44,800 2.152 174,662 39,035 7,685 3.395 11,080 128,000 44,600 3,395 178,195 43.914 10 9,750 5,406 14,765 128,000 44.800 5,005 177,806 48,794 11 12076 6.320 18.396 128.000 O 31.441 159.461 53,673 14.638 7.451 22.589 120.000 0 34 874 162.874 58.552 19.030 10.059 29,089 128,000 0 38,392 165.392 63.432 16 23,000 12.540 36,519 128.000 45.994 169.694 68.351 15 29,276 15,345 45,221 128,000 45,687 173,687 73,190 23 63,432 50.222 113,654 128,000 197.271 07,587 25 87,828 72.555 150,483 128,000 97 917 225.917 97,587 30 92.703 103,929 196,637 128,000 133,413 261,413 97,587 ANB 65 63.432 50,222 113,654 128,000 69271 197.271 97.567 BAND 70 87.628 72.655 160 4.83 120.000 97917 225.917 97,567 ANB 75 92,709 103,929 196,637 128.000 133.413 261,413 97,587 AND 80 97,587 146,377 243,964 120,000 177212 305.212 97,587 CANB 85 128.000 226,400 354.400 128,000 226400 354,400 97,587 BAND 90 128.000 291,104 419.104 120,000 291,104 419,104 97,587 BAB 96 128,000 406,312 534.312 128,000 406,312 534,312 97,587 DANS 100 128,000 548.686 678.000 128.000 548.085 676.006 97,587 Notes: (1) The above is only an ilustration summary of the major benefits of your policy. You are advised to contact your consultant or the Company for more information on this plan. This illustration in no way affects the terms and conditions stated in the Policy Document (2) The above illustration relates only to your Basic Plan excluding any ridors or additional benefits (if applicable). (3) The above values are for illustrative purposes only and assume that all premiums are paid in full when due: (W) no Advanced Claim has been paid, and () the Sum Assured of your Basic Plan remains unchanged throughout the Benefit Term. (4) Terminat Bonus is a one-off bonus payable upon payment of Major Disease Benefit (except for Advanced Claim). Death Bereft, er upon termination of the policy, if any of them occurs from the 5th policy anniversary onwards. The face value of Terminal Bonus will be paid when the Company is paying the Major Disease Benefit or Death Benefit, but only the cash value of Terminal Bonus will be paid when the policy is surrendered in whole or in part. These values are determined and calculated based on the Company's experiences and the current projections of surrender values and bonus scales in relation to a number of factors including, but not limited to claims, persistency and investment assumptions. Hence, the values are not guaranteed and are subject to review and adjustment at the absolute discretion of the Company. You should note that the actual values payable under the policy may differ significantly from the above illustrated values. (5) The Company reserves the right to review the premium rates on each policy anniversary and adjust the premium rates accordingly across a particular risk class. 13 69271 1. Basics. (15) (a) What is the annual premium payment required by this policy? (3) (b) If the policy holder wants to surrender the policy and guarantee the total premium he pays in the last column (assuming survival and not getting major disease), how many years must he wait? If the non-guaranteed terminal bonus is included in the surrender benefit, how many years must he wait to recover the total premium payment? (6) (c) Assume the premium paid by the policyholder can earn an 1% interest rate from an outside asset, and assume the insured survives without getting major diseases. Add a column that calculate the future value of total premium payment at the end of each policy year. (Hint: You may use the NPV function and FV function in Excel. See here for the use of NPV. ](6) 2. Cash value and major disease /death protection. (20) (a) Note that Column (D) lists free 10-year crisis cover amount, which indicates that if the insured dies or gets majaor diseases within 10 years after purchasing the policy, there will be an additional 44,800 USD major disease/death benefit. Calculate the major disease/death protection that this policy provides (based on guaranteed values) 5 years and 20 years after purchasing the policy. (6) (b) What is the "cost" of the free 10-year crisis cover, or, what's the premium level if there is no free 10-year crisis cover? To answer this question, let's make a few simplifying assumptions. (10) Ignore any non-guaranteed terminal bonuses (column E). Assume all premium loadings take place in period 1. Assume a constant discount rate of 2%. For simplicity, we assume the probability of receiving benefit (death + getting major diseases) is the probability of death listed in the Life Table attached (ignore the probability of getting major diseases). Under the assumptions above, please calculate the annual premium payment over the 20 years) if there is no free 10-year crisis cover. This is a hard question, so I provide you with some hint. Hint: You may proceed in the following three steps. First, calculate the probability of receiving the benefit in each year. Second, calculate the premium loading based on the current major disease/death benefit and premium payment as the difference between PV of premium payment and PV of claim cost. Third, using the new major disease/death benefit without the 10-year free crisis cover, calculate the annual premium payment. ] (c) If you want to calculate the premium loading of this policy, what additional information is needed? (4) 3. Policy surrender and policy loans. (15) Suppose Mr Chan has paid premium on time for 15 years. He retired at 60 and his income experienced a large drop. He cannot fulfill the next 5 years of premium payment requirement. He has two options. Option 1: surrender the policy at 60. Option 2: pay 5 more years of premium using policy loans. (a) What is the surrender value of Option 1 (assuming the projected non-guaranteed ter- minal bonus is realized)? (5) (b) Suppose the policy loan requires an interest rate of 5%. What is the cash value that he can receive after he uses policy loan to pay for 5 additional years of premium and surrender at age 65 (assuming survival and no major diseases)? (5) (c) Suppose Mr Chan dies at 65. What is the benefit that the beneficiary can get if Mr Chan chooses option 1 and option 2, respectively at 60? (5) 1 Life Insurance (50') The following table present the cash flow arrangement of a life insurance (including critical illness) policy. Use the information in the table to answer the following questions. Assume all premiums are paid at the beginning of each year, and all payments (death benefit and surrender value) are paid at the end of each year. 0 0 0 1 2 3 4 5 6 O 978 D 9 12 PRUmyhealth lifelong crisis protector IMPORTANT: THIS IS A SUMMARY ILLUSTRATION OF THE BENEFITS OF YOUR POLICY AND IN NO WAY AFFECTS THE TERMS AND CONDITIONS STATED IN THE POLICY DOCUMENT. Name Mr. Chan Tai Man Age Next Birthday (ANB) 45 Sex: Male (Non-smoker) Initial Sum Assured : US$ 128,000 Initial Annual Premium : US$ 4,879.36 Benefit Term : Whole Life Premium Term : 20 years Basic Plan - Hlustration Summary (Currency: USS) Surrender Benefit Major Disease Benefit/ Death Benefit Guaranteed Sum Assured Cash Value of PRUmyhealth Face Value of Guaranteed Non-Guaranteed lifelong crisis Free 10-year Non-Guaranteed End of Cash Value Terminal Bonus Total protector crisis cover Terminal Bonus Total Total Policy Year (A) (B) (A)+(B) (C) (D) (E) (C)+(D)+(E) Premiums 0 0 128,000 44,800 172.600 4,879 0 128,000 44,000 0 172.800 9.750 368 0 368 128.000 44.800 172.800 14,638 976 128.000 44,800 172.800 19,517 1,830 383 2.213 128,000 44,800 1.276 174,076 24,397 2.928 743 3,671 128.000 44.800 1 508 174.305 29.276 7 4,269 1.262 5,531 128.000 44.800 1.748 174,548 34,156 8 5.855 2.152 8,007 128.000 44,800 2.152 174,662 39,035 7,685 3.395 11,080 128,000 44,600 3,395 178,195 43.914 10 9,750 5,406 14,765 128,000 44.800 5,005 177,806 48,794 11 12076 6.320 18.396 128.000 O 31.441 159.461 53,673 14.638 7.451 22.589 120.000 0 34 874 162.874 58.552 19.030 10.059 29,089 128,000 0 38,392 165.392 63.432 16 23,000 12.540 36,519 128.000 45.994 169.694 68.351 15 29,276 15,345 45,221 128,000 45,687 173,687 73,190 23 63,432 50.222 113,654 128,000 197.271 07,587 25 87,828 72.555 150,483 128,000 97 917 225.917 97,587 30 92.703 103,929 196,637 128,000 133,413 261,413 97,587 ANB 65 63.432 50,222 113,654 128,000 69271 197.271 97.567 BAND 70 87.628 72.655 160 4.83 120.000 97917 225.917 97,567 ANB 75 92,709 103,929 196,637 128.000 133.413 261,413 97,587 AND 80 97,587 146,377 243,964 120,000 177212 305.212 97,587 CANB 85 128.000 226,400 354.400 128,000 226400 354,400 97,587 BAND 90 128.000 291,104 419.104 120,000 291,104 419,104 97,587 BAB 96 128,000 406,312 534.312 128,000 406,312 534,312 97,587 DANS 100 128,000 548.686 678.000 128.000 548.085 676.006 97,587 Notes: (1) The above is only an ilustration summary of the major benefits of your policy. You are advised to contact your consultant or the Company for more information on this plan. This illustration in no way affects the terms and conditions stated in the Policy Document (2) The above illustration relates only to your Basic Plan excluding any ridors or additional benefits (if applicable). (3) The above values are for illustrative purposes only and assume that all premiums are paid in full when due: (W) no Advanced Claim has been paid, and () the Sum Assured of your Basic Plan remains unchanged throughout the Benefit Term. (4) Terminat Bonus is a one-off bonus payable upon payment of Major Disease Benefit (except for Advanced Claim). Death Bereft, er upon termination of the policy, if any of them occurs from the 5th policy anniversary onwards. The face value of Terminal Bonus will be paid when the Company is paying the Major Disease Benefit or Death Benefit, but only the cash value of Terminal Bonus will be paid when the policy is surrendered in whole or in part. These values are determined and calculated based on the Company's experiences and the current projections of surrender values and bonus scales in relation to a number of factors including, but not limited to claims, persistency and investment assumptions. Hence, the values are not guaranteed and are subject to review and adjustment at the absolute discretion of the Company. You should note that the actual values payable under the policy may differ significantly from the above illustrated values. (5) The Company reserves the right to review the premium rates on each policy anniversary and adjust the premium rates accordingly across a particular risk class. 13 69271 1. Basics. (15) (a) What is the annual premium payment required by this policy? (3) (b) If the policy holder wants to surrender the policy and guarantee the total premium he pays in the last column (assuming survival and not getting major disease), how many years must he wait? If the non-guaranteed terminal bonus is included in the surrender benefit, how many years must he wait to recover the total premium payment? (6) (c) Assume the premium paid by the policyholder can earn an 1% interest rate from an outside asset, and assume the insured survives without getting major diseases. Add a column that calculate the future value of total premium payment at the end of each policy year. (Hint: You may use the NPV function and FV function in Excel. See here for the use of NPV. ](6) 2. Cash value and major disease /death protection. (20) (a) Note that Column (D) lists free 10-year crisis cover amount, which indicates that if the insured dies or gets majaor diseases within 10 years after purchasing the policy, there will be an additional 44,800 USD major disease/death benefit. Calculate the major disease/death protection that this policy provides (based on guaranteed values) 5 years and 20 years after purchasing the policy. (6) (b) What is the "cost" of the free 10-year crisis cover, or, what's the premium level if there is no free 10-year crisis cover? To answer this question, let's make a few simplifying assumptions. (10) Ignore any non-guaranteed terminal bonuses (column E). Assume all premium loadings take place in period 1. Assume a constant discount rate of 2%. For simplicity, we assume the probability of receiving benefit (death + getting major diseases) is the probability of death listed in the Life Table attached (ignore the probability of getting major diseases). Under the assumptions above, please calculate the annual premium payment over the 20 years) if there is no free 10-year crisis cover. This is a hard question, so I provide you with some hint. Hint: You may proceed in the following three steps. First, calculate the probability of receiving the benefit in each year. Second, calculate the premium loading based on the current major disease/death benefit and premium payment as the difference between PV of premium payment and PV of claim cost. Third, using the new major disease/death benefit without the 10-year free crisis cover, calculate the annual premium payment. ] (c) If you want to calculate the premium loading of this policy, what additional information is needed? (4) 3. Policy surrender and policy loans. (15) Suppose Mr Chan has paid premium on time for 15 years. He retired at 60 and his income experienced a large drop. He cannot fulfill the next 5 years of premium payment requirement. He has two options. Option 1: surrender the policy at 60. Option 2: pay 5 more years of premium using policy loans. (a) What is the surrender value of Option 1 (assuming the projected non-guaranteed ter- minal bonus is realized)? (5) (b) Suppose the policy loan requires an interest rate of 5%. What is the cash value that he can receive after he uses policy loan to pay for 5 additional years of premium and surrender at age 65 (assuming survival and no major diseases)? (5) (c) Suppose Mr Chan dies at 65. What is the benefit that the beneficiary can get if Mr Chan chooses option 1 and option 2, respectively at 60