Future Value of Annuity

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hsmath

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Please verify If I did the right Thing. Thank you so much

You and Jerry are making quarterly investments of $1000 each in a project. The quarterly payments and all early profits are immediately re-invested in the project, with the idea that after 15 years, a corporation will pay you (and other investors) off, and farm the project. The projected interest rate for the project is 12% compounded quarterly.

a. What is your share of the sale at the end of 15 years?

b. Again, what is the effective interest rate you earned?


a) 12% compounded Quaterly , for 15 years N = 15 X 4 = 60 Q

i = 12%/4 = 3% = 0.03

So every quarter the investment amount is applied 3% interest

Quarter
0 1 2 3 60
---+-----------+----------+----------+-------------------+---

ME 1000 1000 1000 1000


Jerry 1000 1000 1000 1000


Total 2000 2000 2000 2000


Find FV of each investment period which is compounded quarterly


Annuity FV factor = (Future value factor -1)/r
= [(1 + r)^t - 1]/r
= [ (1 + 0.03)^60 - 1 ] /.03
=163.053436
= 163.0534

For Annuity Future value for Annuity 2000 ,15 years compounded Quarterly @ 12 %
= 2000 X 163.0534
= $ 326106.8

Since me and Jerry had invested each $1000

My share at the end of 15 years will be $ 326106.8/2 = $163053.4

I get $$163053.4 for investing a Total of 60 X $1000 = $60,000

Question : DId i go it right ?
Why does Jerry need to be involved in my calculation. I could have even done the same for my investment of $1000, Do I need to take the total of
$2000 for me and Jerry and then do the calculation ??

b) Effective Interest Rate for 12% quarterly compounding
i = (1 + r/M)^M - 1
= (1 + 0.12/4) ^ 4 - 1
= ( 1 + 0.03) ^4 -1
= 12.550881 %

Question : Is the above Effective Interest rate correct ?
 
Which part did you do wrong on purpose?

Did you make your payments at the beginning of each quarter or at the end? You MUST be able to answer this question.

It looks good, except that the previous question needs to be answered. Why do you doubt?
 
Thanx tkhunny for your response.

Payments I beleive are at the end of the period ...ordinary annuity.

i doubt because I am a Novice in fianance I spent 8 hours full night with no sleep trying to solve this.

I did not understand what jerry has to do with my investment since both of us are investing same amount individually.
 
Well, I simply "shudder" at a teacher wording a simple problem in such words!
Really, the problem simply is:
1: what is future value of $1000 deposited quarterly for 15 years, at rate of 12% compounded quarterly ?
2: what is the effective annual rate?
 
hsmath said:
Payments I beleive are at the end of the period ...ordinary annuity.
Click to expand...
You'ld have to convince me that "ordinary annuity" = "annuity immediate" in general. That language may have fallen out of favor in the real world. Personally, I don't even like "annuity due" or "annuity immediate". Why not just specify where the payments are? So much less confusing - even to the "man on the street". Really, why develop jargon when simple language already exists?

I know. I'm a rebel.
 
So did I do the right thing here ?

Please comment on the solution assuming ordinary annuity. Just keep it simple. I had never heard of the word annuity before I started learning finance.
 
That's where I started this conversation. Did you do part of it incorrectly on purpose? If not, why do you doubt. You did fine.
 
Oh Ok Thanx for saying I did fine.

I just tried to solve it with my limited Fin knowledge.

I could have got the same answer even without Jerry being involved.

Thanx all for your help
 
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