An insurer issued a large number of policies to people age 50. Each policy is a 30-year endowmentinsurance with a benefit of $100,000 and an annual gross premium of $2,500 payable for 20 years.The insurer’s reserving basis is:Standard Ultimate Life Table at 5% (the one that I distributed in class).Expenses are 20% of the first premium, 5% of subsequent premiums, $200 upon payment of deathbenefit, $50 upon payment of endowment benefit.Ten years after issue, a total of 100 of these policies were still in force (for people now age 60).In the following year:Expenses of 4% of each premium were incurred,interest of 4.5% was earned on all assets,one policyholder died, andexpenses of $150 were incurred on the payment of the benefit of the one policyholder that died.(a) Calculate the profit or loss on this group of policies for this year.(b) Determine how much of this profit/loss is attributable to interest, expenses and mortality (in thatorder)(c) Determine how much of this profit/loss is attributable to expenses, interest and mortality (in thatorder)Guidance: This problem is similar to example 7.8 on P239 in the textbook (3rd edition) and example 7 from class. Use themas guides. But there are some differences. Be careful! (for example: the change in terminal expenses between the insurancebenefit and the endowment benefit. The table gives an APV of 20-year endowment insurance but not insurance alone. Whatwill you do?). Also, do not attempt to verify the given gross premium of $2,500 using the reserving basis. It was notcalculated by that basis. You are not given the pricing basis. Just go with the premium that you are given. - JS An insurer issued a large number of policies to people age 50. Each policy is a 30-year endowmentinsurance with a benefit of $100,000 and an annual gross premium of $2,500 payable for 20 years.The insurer's reserving basis is:Standard Ultimate Life Table at 5% (the one that I distributed in class).Expenses are 20% of the first premium, 5% of subsequent premiums, $200 upon payment of deathbenefit, $50 upon payment of endowment benefit.Ten years after issue, a total of 100 of these policies were still in force (for people now age 60).In the following year:Expenses of 4% of each premium were incurred,interest of 4.5% was earned on all assets,one policyholder died, andexpenses of $150 were incurred on the payment of the benefit of the one policyholder that died.(a) Calculate the profit or loss on this group of policies for this year.(b) Determine how much of this profit/loss is attributable to interest, expenses and mortality (in thatorder)(c) Determine how much of this profit/loss is attributable to expenses, interest and mortality (in thatorder)Guidance: This problem is similar to example 7.8 on P239 in the textbook (3rd edition) and example 7 from class. Use themas guides. But there are some differences. Be careful! (for example: the change in terminal expenses between the insurancebenefit and the endowment benefit. The table gives an APV of 20-year endowment insurance but not insurance alone. Whatwill you do?). Also, do not attempt to verify the given gross premium of $2,500 using the reserving basis. It was notcalculated by that basis. You are not given the pricing basis. Just go with the premium that you are given. - JS

This question is about calculating the profit or loss of a group of policies issued by an insurer to…

An insurer issued a large number of policies to people age 50. Each policy is a 30-year endowment insurance with a benefit of $100,000 and an annual gross premium of $2,500 payable for 20 years. The insurer’s reserving basis is: Standard Ultimate Life Table at 5% (the one that I distributed in class). Expenses are 20% of the first premium, 5% of subsequent premiums, $200 upon payment of death benefit, $50 upon payment of endowment benefit. Ten years after issue, a total of 100 of these policies were still in force (for people now age 60). In the following year: Expenses of 4% of each premium were incurred, interest of 4.5% was earned on all assets, one policyholder died, and expenses of $150 were incurred on the payment of the benefit of the one policyholder that died. (a) Calculate the profit or loss on this group of policies for this year. (b) Determine how much of this profit/loss is attributable to interest, expenses and mortality (in that order) (c) Determine how much of this profit/loss is attributable to expenses, interest and mortality (in that order) Guidance: This problem is similar to example 7.8 on P239 in the textbook (3rd edition) and example 7 from class. Use them as guides. But there are some differences. Be careful! (for example: the change in terminal expenses between the insurance benefit and the endowment benefit. The table gives an APV of 20-year endowment insurance but not insurance alone. What will you do?). Also, do not attempt to verify the given gross premium of $2,500 using the reserving basis. It was not calculated by that basis. You are not given the pricing basis. Just go with the premium that you are given.

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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An insurer issued a large number of policies to people age 50. Each policy is a 30-year endowment
insurance with a benefit of $100,000 and an annual gross premium of $2,500 payable for 20 years.
The insurer’s reserving basis is:
Standard Ultimate Life Table at 5% (the one that I distributed in class).
Expenses are 20% of the first premium, 5% of subsequent premiums, $200 upon payment of death
benefit, $50 upon payment of endowment benefit.
Ten years after issue, a total of 100 of these policies were still in force (for people now age 60).
In the following year:
Expenses of 4% of each premium were incurred,
interest of 4.5% was earned on all assets,
one policyholder died, and
expenses of $150 were incurred on the payment of the benefit of the one policyholder that died.
(a) Calculate the profit or loss on this group of policies for this year.
(b) Determine how much of this profit/loss is attributable to interest, expenses and mortality (in that
order)
(c) Determine how much of this profit/loss is attributable to expenses, interest and mortality (in that
order)
Guidance: This problem is similar to example 7.8 on P239 in the textbook (3rd edition) and example 7 from class. Use them
as guides. But there are some differences. Be careful! (for example: the change in terminal expenses between the insurance
benefit and the endowment benefit. The table gives an APV of 20-year endowment insurance but not insurance alone. What
will you do?). Also, do not attempt to verify the given gross premium of $2,500 using the reserving basis. It was not
calculated by that basis. You are not given the pricing basis. Just go with the premium that you are given. - JS

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