• We are pleased to announce that the winner of our Feedback Prize Draw for the Winter 2024-25 session and winning £150 of gift vouchers is Zhao Liang Tay. Congratulations to Zhao Liang. If you fancy winning £150 worth of gift vouchers (from a major UK store) for the Summer 2025 exam sitting for just a few minutes of your time throughout the session, please see our website at https://www.acted.co.uk/further-info.html?pat=feedback#feedback-prize for more information on how you can make sure your name is included in the draw at the end of the session.
  • Please be advised that the SP1, SP5 and SP7 X1 deadline is the 14th July and not the 17th June as first stated. Please accept out apologies for any confusion caused.

Calculation doubt

1

1495_sc

Ton up Member
Hello,

Can someone please share the workings of example question in study material for Alterations section 3.2? We need to calculate the paid up sum assured. My workings are below but my answer doesn't match with the material i.e 10,655. I haven't worked on endowment assurance/annuity formula since a very long time so I think I need help with the formula.

8880= (PUSA)*Abar:[45]:<5> + 25*adue:[45]:<5>

8880= (PUSA)*(1-ln1.04*(adue:[45]:<5>-0.5)) +25*adue:[45]:<5>

adue:[45]:<5>= adue:[45]- v^(5)* 5p[45]*adue:50

=18.829-1.05^(-5)*(9712.0728/9798.0837)*17.444= 5.28115

=>8880= (PUSA)*0.81248+132.02875

=>PUSA=10767.00037

Thank you in advance!
 
Hi - haven't looked at this in any detail, but the issue might be that you seem to be using 1.05^(-5) rather than 1.04^(-5) about halfway down? (the interest rate is 4%)
 
Hello,

Thank you for identifying this issue. Revised calculation is below.
It still doesn't tie with the study material's solution. Perhaps the ambiguous part is the formula for Abar:x:<n>

I expanded it as 1- ln(1+i)*abar:x:<n>
= 1-ln(1+i)*(adue:x:<n>-0.5)

Can you only confirm if abar:x:<n> = adue:x:<n>-0.5 ? If not, how to calculate abar:x:<n> or Abar:x:<n>?

8880= (PUSA)*Abar:[45]:<5> + 25*adue:[45]:<5>

8880= (PUSA)*(1-ln1.04*(adue:[45]:<5>-0.5)) +25*adue:[45]:<5>

adue:[45]:<5>= adue:[45]- v^(5)* 5p[45]*adue:50

=18.829-1.04^(-5)*(9712.0728/9798.0837)*17.444=

4.617165

=>8880= (PUSA)*0.83852+115.4291

=>PUSA=10452.4059

Regards
 
Tried it again as follows to get PUSA= 10654 vs 10658 in study material (close enough, I think)

Formula to confirm now-

Abar:x:<n>= TAbar:x:<n>+ PE:x:<n>

derived from
Abar:x= (1+i)^(0.5)*A:x

8880= (PUSA)*Abar:[45]:<5> + 25*adue:[45]:<5>

=>8880= (PUSA)*(Tabar:[45]:<5>+v^(5)*5p[45]*A:50) +25*adue:[45]:<5>

=>8880= (PUSA)*(1.04)^(0.5)*((A:[45]-1.04^(-5)*(9712.0728/9798.0837)*A:50))+1.04^(-5)*(9712.0728/9798.0837) +25*adue:[45]:<5>

=PUSA*(1.04)^(0.5)*((0.27583-1.04^(-5)*(9712.0728/9798.0837)*0.32907)) +1.04^(-5)*(9712.0728/9798.0837)+25*adue:[45]:<5>

=PUSA*0.8226+25*adue:[45]:<5>

adue:[45]:<5>= adue:[45]- v^(5)* 5p[45]*adue:50

=18.829-1.04^(-5)*(9712.0728/9798.0837)*17.444=

4.617165

=>8880= (PUSA)*0.8226+115.4291

=>PUSA=10654.74
 
Well done - that looks good!

FWIW I think the problem before was in your abar formula. Should have been:

abar(x:n) ≈ adue(x:n) - 0.5 x [1 - D(x+n)/D(x)]
 
You must log in or register to reply here.
Back
Top