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Clarify the answer from Q&A Bank Part 1

Hi,
there is a question asking whether "S due (n+1) = 1 + Sn" is true or not?
The answer from this question is it is not true, and it gave that "S due (n+1) = (1+i)^n + Sn". However, I can't clarify this. I can only show that "S(n+1) = (1+i)^n + Sn". Does the answer given is incorrect? or I actually my own answer is incorrect?

Please correct me, because these type of concept struggle me a lots!

Thanks for your help.

Cheers,
Jacq

 

I think all of the above formula is wrong! (But i could be wrong!!!)

Haven't done this subject for a couple of years now, but I think your answer may be wrong.
I would suggest that:

S(n+1) = 1 + S(n)*(1+i)


Surely the difference between S(n+1) and S(n) is that S(n+1) is compounded one year extra into the future - both start at the same time, hence we get S(n)*(1+i), but S(n+1) also has one additional payment at the end of the final year, (which therefore recieves no interest) hence +1.

Since both our formulae involve only s(n) (and not S due), you can check this by working through a practical example using the values for S(n) and S(n+1), from the actuarial tables.

The reason why:

S due (n+1) = 1 + Sn, is false is because:

The RHS has not been compounded at all (which it needs to be), to reflect that S due (n+1) earns an extra years interest on all payments than S(n) (since payments are made one year earlier).

The correct answer is in my opinion is : S due (n+1) = (1+i)^(n+1) + S(n)*(1+i)

E.g.

S(4) = (1+i)^3 + (1+i)^2 + (1+i) + 1

S due (4+1) = (1+i)^5 + (1+i)^4 + (1+i)^3 + (1+i)^2 + (1+i)

= (1+i)^5 + (1+i) * [ (1+i)^3 + (1+i)^2 + (1+i) + 1 ]

= (1+i)^(4+1) + (1+i)*S(4)

=(1+i)^(n+1) + (1+i)*S(n)

So it would seem I do not agree with the given solution either. Perhaps a tutor could clatify for us?

Hope that helps!

 

the original expression in the question: sdue(n+1)=1+s(n) is wrong.

The alternative in the solution is also wrong: sdue(n+1)=(1+i)^n+s(n)

The two alternatives you give are both correct.
so s(n+1)=(1+i)^n + S(n)
and sdue(n+1) = (1+i)^(n+1) + (1+i)S(n)

since the second is just the first multiplied by (1+i).

The nice relationship which I expect the original was supposed to be a "play" on is:
s(n+1) = 1 + sdue(n)

 

Hi John,

Just in chapter 3 now. Does this apply to the 2011 content as well?

Kippy

 

I remember when I studied CT1 (sat it in April 2010), I really struggled with Chapter 3 initially. It was at that point, I was thinking "what have I let myself in for!"

 

Where do we find this?

Thanks