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)]
