# S.O.S. Mathematics CyberBoard

Your Resource for mathematics help on the web!
 It is currently Fri, 24 May 2013 13:38:47 UTC

 All times are UTC [ DST ]

 Page 1 of 1 [ 7 posts ]
 Print view Previous topic | Next topic
Author Message
 Post subject: Re-write equation in terms of iPosted: Thu, 8 Mar 2012 06:26:35 UTC
 Member

Joined: Sun, 5 Feb 2012 21:05:29 UTC
Posts: 18
Hi,

Can someone tell me how to re-write this equation in terms of i, thanks.

(1+i)^15 - 1 / 1 - (1+i)^15 = 37804.39/15077.10

Top

 Post subject: Re: Re-write equation in terms of iPosted: Thu, 8 Mar 2012 06:37:07 UTC
 Moderator

Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12103
Location: Austin, TX
Hi,

Can someone tell me how to re-write this equation in terms of i, thanks.

(1+i)^15 - 1 / 1 - (1+i)^15 = 37804.39/15077.10

There is a mistake in what you have written. No matter how I put in parentheses this is impossible as written.

_________________
(\ /)
(O.o)
(> <)
This is Bunny. Copy Bunny into your signature to help him on his way to world domination

Top

 Post subject: Re: Re-write equation in terms of iPosted: Thu, 8 Mar 2012 06:45:46 UTC
 Member

Joined: Sun, 5 Feb 2012 21:05:29 UTC
Posts: 18
It should be correct. I have simplified a bit. But the equation is correct. Perhaps seeing the question will clarify the equation I wrote.

Matt inherited as a trust of a fifteen-year annuity-immediate with annual payments. He has been told that the
annuity payments earn compound interest at a level rate and that at the end of fifteen years, their accumulated
value will be $37,804.39. He has further been assured that figured at this same rate of interest, the value of his inheritance was$15,077.10. The trust executor will not reveal the amount of annual payments. Determine this
amount and also the annual effective interest rate earned by the annuity payments.

(1+i)^15 - 1 / 1 - (1+i)^15 = 37804.39/15077.10

The equation of s angle n is [(1+i)^n]/i.

and the equation of a angle n is [1-(1+i)^n]/i. The i's cancel out to give you the above equation. Please let me know if that is not right.

Top

 Post subject: Re: Re-write equation in terms of iPosted: Thu, 8 Mar 2012 15:52:13 UTC
 Moderator

Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12103
Location: Austin, TX
It should be correct. I have simplified a bit. But the equation is correct. Perhaps seeing the question will clarify the equation I wrote.

Matt inherited as a trust of a fifteen-year annuity-immediate with annual payments. He has been told that the
annuity payments earn compound interest at a level rate and that at the end of fifteen years, their accumulated
value will be $37,804.39. He has further been assured that figured at this same rate of interest, the value of his inheritance was$15,077.10. The trust executor will not reveal the amount of annual payments. Determine this
amount and also the annual effective interest rate earned by the annuity payments.

(1+i)^15 - 1 / 1 - (1+i)^15 = 37804.39/15077.10

The equation of s angle n is [(1+i)^n]/i.

and the equation of a angle n is [1-(1+i)^n]/i. The i's cancel out to give you the above equation. Please let me know if that is not right.

The equation cannot be right, first of all--as written, the left-hand side is just -1, and we can all agree -1 is not equal to 37804.39/15077.1 as the latter is positive.

_________________
(\ /)
(O.o)
(> <)
This is Bunny. Copy Bunny into your signature to help him on his way to world domination

Top

 Post subject: Re: Re-write equation in terms of iPosted: Thu, 8 Mar 2012 16:32:06 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Sun, 24 Jul 2005 20:12:39 UTC
Posts: 3692
Location: Ottawa Ontario
didn't check but I think due to lack of proper bracketing...

Anyway, here's how I'd attack your problem:

Step#1: determine the rate:
15077.10(1 + i)^15 = 37804.39
i = (37804.39 / 15077.10)^(1/15) - 1 ; .0632 or 6.32%

Now you're left with calculating the annual payment;
same as a loan of 15077.10 over 15 years at annual interest = 6.32%.
Formula:
P = Ai / [1 - (1+i)^(-n)]
where:
P = Payment (?)
A = Amount borrowed (15077.10)
n = number of payments (15)
i = interest (.0632)

P = 15077.10 * .0632 / [1 - 1.0632^(-15)] = 1585.00

Surprisingly no cents in the payment!

_________________
I'm not prejudiced...I hate everybody equally!

Top

 Post subject: Re: Re-write equation in terms of iPosted: Thu, 8 Mar 2012 16:34:39 UTC
 Moderator

Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12103
Location: Austin, TX
Denis wrote:
didn't check but I think due to lack of proper bracketing...

Anyway, here's how I'd attack your problem:

Step#1: determine the rate:
15077.10(1 + i)^15 = 37804.30
i = (37804.39 / 15077.10)^(1/15) - 1 ; .0632 or 6.32%

Now you're left with calculating the annual payment;
same as a loan of 15077.10 over 15 years at annual interest = 6.32%.
Formula:
P = Ai / [1 - (1+i)^(-n)]
where:
P = Payment (?)
A = Amount borrowed (15077.10)
n = number of payments (15)
i = interest (.0632)

P = 15077.10 * .0632 / [1 - 1.0632^(-15)] = 1585.00

Surprisingly no cents in the payment!

Maybe, but I couldn't figure out a bracketing where it actually worked, parentheses the first two terms, or both pairs and you still get -1 on the LHS. It would be less highly trivial if it were just the last two terms, I suppose, then you have which at least could be solved.

_________________
(\ /)
(O.o)
(> <)
This is Bunny. Copy Bunny into your signature to help him on his way to world domination

Top

 Post subject: Re: Re-write equation in terms of iPosted: Thu, 8 Mar 2012 16:53:39 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Sun, 24 Jul 2005 20:12:39 UTC
Posts: 3692
Location: Ottawa Ontario
This is what the "account" will look like:
Code:
YEAR   PAYMENT       INTEREST       BALANCE
0                                  15,077.10
1      1,585.00        952.87      14,444.97
2      1,585.00        912.92      13,772.89
.....
14     1,585.00        182.83       1,490.79
15     1.585.00         94.21            .00

It is same as a loan: the Bank is theoretically borrowing from you
and paying you back in annual payments: capish?

Equation (once more!):
P = Ai / [1 - (1+i)^(-n)] where i = (37804.39 / A)^(1/n) - 1

_________________
I'm not prejudiced...I hate everybody equally!

Top

 Display posts from previous: All posts1 day7 days2 weeks1 month3 months6 months1 year Sort by AuthorPost timeSubject AscendingDescending
 Page 1 of 1 [ 7 posts ]

 All times are UTC [ DST ]

#### Who is online

Users browsing this forum: No registered users

 You cannot post new topics in this forumYou cannot reply to topics in this forumYou cannot edit your posts in this forumYou cannot delete your posts in this forum

Search for:
 Jump to:  Select a forum ------------------ High School and College Mathematics    Algebra    Geometry and Trigonometry    Calculus    Matrix Algebra    Differential Equations    Probability and Statistics    Proposed Problems Applications    Physics, Chemistry, Engineering, etc.    Computer Science    Math for Business and Economics Advanced Mathematics    Foundations    Algebra and Number Theory    Analysis and Topology    Applied Mathematics    Other Topics in Advanced Mathematics Other Topics    Administrator Announcements    Comments and Suggestions for S.O.S. Math    Posting Math Formulas with LaTeX    Miscellaneous