Annuities payable pthly

In Chp 6 the derivation for annuities payable pthly isn't clear to me.. Could someone pls explain.
I can slove the sums well enough in this so should i still bother myself with the derivation of the formula in this part?

 

The syllabus objective says we must be able to derive the annuity formulas (including those that are pthly) in terms of i, v, n, d, delta, i(p) and d(p).

I believe that it's sufficient here to know that:

a_n = (1-v^n)/i
a(p)_n = (1-v^n)/i(p)
and so on

I don't think it's a requirement of the syllabus to prove that a_n = (1-v^n)/i.

Hope that helps (and if I'm wrong somebody better tell me fast!)

Tim

 

Thanks.. I followed the derivation

However I have another query from the same chp
Q6.8
Find the present value as at 1 June 2004 of payments of £1,000 payable on the first day of each month from July 2004 to December 2004 inclusive, assuming a rate of interest of 8% per annum convertible quarterly.

Since the sum mentions "first day of each month" shouldn't we be using A due N instead of A.N. because the soln used A.N.

 

but the answer via the two approaches are different, as in via

A.N it is : 5863

A due N it is : 5786

So it that still acceptable?

 

question 6.8

Dear Visaka,

Good day! Could you please help me out in solving question 6.8. In question, we are payments are made in advance. While we use convertible quarterly method, why is the solution given by using A_n rather than A due n. I hope for a discussion soon. I am stuck here.

Thank you for your time.

Regards,
Kunal Verma

 

dear all,
i hope u must hv been cleared the solution for Q. 6.8 -CT1
u can go thru following also-(considering for 1 complete year)-
PV= 12000*(v^(1/p))* (A due n pthly)
= 12000*(v^(1/p))*(1-v^n)/d(12)
putting the numericals--
i=0.08 (given)
v=0.923845
d(12)=0.078950
p=12
u'll get PV=12000*0.4886=5863.35