Pension Fund-Denominator function

Up to some limit am able to derive and calculate the sums related to pension scheme.
But in some cases am not able to use correct functions ( only in denominator ). I have checked almost all the sums from past exams, but can not make it.
My Query ...
1) When or in which case to use \(^sD_x\) and \(S_{x-1} * D_{x}\) in the denominator?


2) When to use \(S_{x}/S_{x-1}\) ?

Kindly help on urgent basis...

 

Help

 

Tutor?

 

Is there anyone able to help?

 

sDx = sx*Dx

Suppose, the salary S is for year [x-1,x]

then the past year service benefit for retirement is equal to as follows:
[ m(past years of service)*S(final year salary)*zMra(function at age x) ] / [ 60(suppose)*s(x-1)(since S referring to salary for [x-1,x]) * Dx

{in the EPV formulas given in the mat, we see that there is no sDx in the general formulas}

So, we can rewrite it as:

after multiplying (sx) in both numerator and denominator,

[ m(past years of service)*S(final year salary)*zMra(function at age x) ] *sx / [ 60(suppose)*s(x-1)(since S referring to salary for [x-1,x]) * Dx *sx

now, sxDx = sDx (as given in the tables)

So,

[ m(past years of service)*S(final year salary)*zMra(function at age x) ]* sx / [ 60(suppose)*s(x-1)(since S referring to salary for [x-1,x]) * sDx

so we get,

[ m*S*(zMra at age x) ]*sx / [ 60*sDx* s(x-1) ]

even if we don't multiply sx in both numerator and denominator, we can get the correct answer, provided we use Dx instead of sDx in that case.

Hope this helps!
regards,
Shyam