how to write bonus expression increasing sum assured

[dextar]

Hello

Please help me in writing the expression for sum assured, if it increases or decreases. For example
Q 2.27 in Q&A bank part 2

Please advise how RHS of the solution is showing

9800A[40]:20 +200 IA 1 [40]:20 +4200 D60/D[40]

Any derivation pointers would be useful

 

[KeyurShah]

EPV of Benefits = 9800A 1[40]:20 + 200 (iA) 1[40]:20 + 14000 A[40]:20_1

Now, we can split the pure endowment part of benefits into two separate pure endowment benefits, one with maturity amount 9800 and the other with 4200.

= 9800A 1[40]:20 + 200(IA) 1[40]:20 + 9800 A[40]:20_1 + 4200 A[40]:20_1

We can add up the term assurance (the first expression) and the pure endowment assurance with maturity amount 9800 (the third expression) to give us an endowment assurance with benefit of 9800.

= 9800 A [40]:20 + 200 (IA) 1[40]:20 + 4200 A[40]:20_1

which is the final expression given in the solution to the question in QB.

Hope this solves your doubt.

 

[dextar]

EPV of Benefits = 9800A 1[40]:20 + 200 (iA) 1[40]:20 + 14000 A[40]:20_1

Now, we can split the pure endowment part of benefits into two separate pure endowment benefits, one with maturity amount 9800 and the other with 4200.

= 9800A 1[40]:20 + 200(IA) 1[40]:20 + 9800 A[40]:20_1 + 4200 A[40]:20_1

We can add up the term assurance (the first expression) and the pure endowment assurance with maturity amount 9800 (the third expression) to give us an endowment assurance with benefit of 9800.

= 9800 A [40]:20 + 200 (IA) 1[40]:20 + 4200 A[40]:20_1

which is the final expression given in the solution to the question in QB.

Hope this solves your doubt.

Hello Thanks for the help. However, I haven't followed the approach. I want to know why the figure of 9800 is coming?

WOuld you please start from the basic. It says 10,000 at the end of year
So ideally 10,000vq|x+..... so how did we arrive at 9800?

 

[KeyurShah]

Let's look at the way these payments will be made at the end of each year if the policyholder dies in that year.

Year 0-1: 10,000 = 9,800 + 200
Year 1-2: 10,200 = 9,800 + (2*200)
Year 2-3: 10,4000 = 9,800 + (3*200)
and so on..
If he dies in Year 19-20: 13,800 = 9,800 + (19*200)

Thus if you see the pattern of payments, the payment of 9,800 is constant for each year, and hence it is a LEVEL term assurance of 9,800.

The other part of each payment is a SIMPLE INCREASING term assurance of 200.

Now, if he survives the entire term of the contract, there is going to be a bonus announcement at the end of 20th Year.

And hence the maturity amount will be 13,800 plus 200 i.e 14,000 which will be calculated using pure endowment function.

 

[KeyurShah]

Let's look at the way these payments will be made at the end of each year if the policyholder dies in that year.

Year 0-1: 10,000 = 9,800 + 200
Year 1-2: 10,200 = 9,800 + (2*200)
Year 2-3: 10,4000 = 9,800 + (3*200)
and so on..
If he dies in Year 19-20: 13,800 = 9,800 + (20*200) <= Correction

Thus if you see the pattern of payments, the payment of 9,800 is constant for each year, and hence it is a LEVEL term assurance of 9,800.

The other part of each payment is a SIMPLE INCREASING term assurance of 200.

Now, if he survives the entire term of the contract, there is going to be a bonus announcement at the end of 20th Year.

And hence the maturity amount will be 13,800 plus 200 i.e 14,000 which will be calculated using pure endowment function.

 

[dextar]

Thanks a lot for thie explanation. It is much clear now.

BTW if he dies in year 19-20 then he will get 9800+ 20*200= 13800. i think this summarizes the 14000 figure after having one more bonus.

 

[KeyurShah]

I'm glad I could help you.

 

[dextar]

Question3.21 Q&A bank part 3

Hello

would anyone please explain the solution ,why the second part is required.

in EPV

The first integral in the solution should be enough? what information the second part captures as we are already integarting from 10 to 15?