Mortgage Payment Schedule beginning, mortgage, principal

irlfaan7

I had glossed over it before because I thought I knew this but coming back to it, I have a question:

We pay monthly payment at the beginning of every month. Then the first payment should have 0 interest component (as happens in case of capital leases) and the entire payment should go toward reducing the principal. But that doesn't happen. We calculate as if we were paying at the end of every month. Any reason why this is so?

If you calculate PV given monthly mortgage payment, i and number of years in the BEGIN mode, the PV comes out to be higher than given.
Say,
PMT = 742.50
i = 8.125/12
n = 360 (for 30 yrs)
FV = 0
PV you get as 100,677.47 in BEGIN mode (not 100,000 as you would get in the end mode)
See page 403 of curriculum.

What am I missing?

marsilni

thisisbrianly Wrote:
-------------------------------------------------------
> anish, I'm not exactly sure what your question
> is....are you just trying to understand why the PV
> of a payment stream with payments in the beginning
> of the month is more than the same payment stream
> at the end? I'm not sure, byt maybe this will
> help - the difference between the "ending period"
> stream and "begin" is that all the payments
> essentially get made 30-days earlier in the
> "begin" stream.
>
> The only payments that are affected by "beg or
> end" are the 1st payment (which occurs at T0 for
> the "beg" stream instead of T1 for "end") and the
> last payment (which occurs 30-days earlier for the
> "beg" stream). The timing of all the other
> payments are identical since the "end" of T1 is
> the same as the "beginning" of T2, "end of T3 =
> beg of T4", etc.
>
> The difference between the PV of the two streams
> is $677. This is completely accounted for by the
> difference in PV between the T0 and T360
> payments:
>
> The PV T0 payment is obviously $742.50.
> The PV T360 is:
> n = 360
> i = 8.125/12
> FV = 742.5
> Calc PV = $65.41
>
> $742 - 65 = $677
>
> Again, not sure if I answered your question, but
> hopefully the explanation above helps. Just
> remember that the only things that are different
> about "beg" and "end" streams is the timing of
> first and last payments...all the other payments
> are basically the same.
>

Thanks for your response Brian. Actually my question is 'We pay monthly mortgage payment at the beginning of every month. Then the first payment (month 1) should have 0 interest component (as happens in case of capital leases) and the entire payment should go toward reducing the principal. But that doesn't happen. Why?'

I am sorry if I was unclear before.

ftwcfa

I don't have the curriculum on me right now but why would you make a mortgage payment at t=0? That's like taking a loan today and repaying some immediately which sounds kinda silly to me....



Edited 1 time(s). Last edit at Thursday, May 19, 2011 at 08:01PM by Cinderella.

Maddin

Anish,

Not sure if I understand your question correctly but here is my explanation.
Lets say you take a mortgage out on 1st June. Your first payment is due on 1st July. If you consider the date June 1st as T=0 then your mortgage payment is due @T=1. Therefore your calculation will be based on "end" mode and interest will be paid for the 1st month and not as you indicated like a cap lease. Hope this helps.

kd26gioi

Kiakaha Wrote:
-------------------------------------------------------
> Anish, are you sure it's paid at the start of the
> month?

That's what I gathered from: CFA Curriculum, Vol 5, Page 402, first line
What do you think?

Brian: Let me review it again. May be it will make sense tomorrow. Thanks for your help.

Bluetick1010

C3Po Wrote:
-------------------------------------------------------
> Anish,
>
> Not sure if I understand your question correctly
> but here is my explanation.
> Lets say you take a mortgage out on 1st June. Your
> first payment is due on 1st July. If you
> consider the date June 1st as T=0 then your
> mortgage payment is due @T=1. Therefore your
> calculation will be based on "end" mode and
> interest will be paid for the 1st month and not as
> you indicated like a cap lease. Hope this helps.


Right. It makes sense. Thanks C3Po