A
ActStudent1405
Member
The method I used to calculate the expected present value of premiums for Scenario 3 is different from that in the model answer. As an illustration I used the EPV Premiums for age 50.
(1) Before option date – all policies
The period before the option is equivalent to a term policy. The EPV of premiums for the first ten years for all policies is:
äx:10 * P x:10 * Sum Assured - using standard mortality rates
Answer I got is: £337.34
(2) After option date – policyholders taking up option – Basic Sum Assured
This is equivalent to a new whole of life policy at standard premium rates
ä60 * P60 * v10 * 10px * 0.7 * Sum Assured - using standard mortality rates
Answer: £1,928.67
(3) After option date – policyholders taking up option – Basic Sum Assured
This is equivalent to a new whole of life policy at standard premium rates
ä60 (at higher mortality rates) * P60 (standard mortality rates) * v10 * 10px (standard mortality rates) * 0.3 * Sum Assured
Answer: £683.58
(4) After option date – policyholders taking up option – Additional Sum Assured
This is equivalent to a new whole of life policy at standard premium rates
ä60 (at higher mortality rates) * P 60 (standard mortality rates) * v10 * 10px (standard mortality rates) * 0.3 * Sum Assured
Answer: £683.58
Summing these values gives an answer of £3,633.16, This is different from the model answer. For policyholder taking up the options: adding £337.34 * 0.7 + £1,928.67 = £2,164.82 which is part of the answer in cell R11 of the worksheet titled Rated in the model solutions. The premium paid by policyholders taking up the option for the additional sum assured in (4) tallies with the model answer. My guess is that something is not correct in part (3). Any help is appreciated.
(1) Before option date – all policies
The period before the option is equivalent to a term policy. The EPV of premiums for the first ten years for all policies is:
äx:10 * P x:10 * Sum Assured - using standard mortality rates
Answer I got is: £337.34
(2) After option date – policyholders taking up option – Basic Sum Assured
This is equivalent to a new whole of life policy at standard premium rates
ä60 * P60 * v10 * 10px * 0.7 * Sum Assured - using standard mortality rates
Answer: £1,928.67
(3) After option date – policyholders taking up option – Basic Sum Assured
This is equivalent to a new whole of life policy at standard premium rates
ä60 (at higher mortality rates) * P60 (standard mortality rates) * v10 * 10px (standard mortality rates) * 0.3 * Sum Assured
Answer: £683.58
(4) After option date – policyholders taking up option – Additional Sum Assured
This is equivalent to a new whole of life policy at standard premium rates
ä60 (at higher mortality rates) * P 60 (standard mortality rates) * v10 * 10px (standard mortality rates) * 0.3 * Sum Assured
Answer: £683.58
Summing these values gives an answer of £3,633.16, This is different from the model answer. For policyholder taking up the options: adding £337.34 * 0.7 + £1,928.67 = £2,164.82 which is part of the answer in cell R11 of the worksheet titled Rated in the model solutions. The premium paid by policyholders taking up the option for the additional sum assured in (4) tallies with the model answer. My guess is that something is not correct in part (3). Any help is appreciated.