Results 1 to 12 of 12
Like Tree2Thanks
  • 1 Post By jonah
  • 1 Post By catenary

Math Help - Annuity Problem - deferred

  1. #1
    Newbie
    Joined
    Aug 2014
    From
    Philippines
    Posts
    2

    Annuity Problem - deferred

    A mother borrowed 100000 with 2% interest monthly and promised to pay the amount by 30 equal monthly installments starting 1 year from now. Determine the monthly payment.

    a. 5551.66 c. 7551.66
    b. 6551.66 d. 8551.66

    thanks....
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Feb 2014
    From
    Negros
    Posts
    110
    Thanks
    7

    Re: Annuity Problem - deferred

    First you need to get what the cash balance would be 11 months from now using F = P(1 + i)^{(m*n)}. Then use the formula A = P*\dfrac{(\dfrac{r}{m})(1+\dfrac{r}{m})^{(m*n)}}{(  1+\dfrac{r}{m})^{(m*n)} - 1} where r is the nominal rate of interest which from your problem is 2%, n is the time in years, m is the number of times compounded in one year so in this case 12. However the answer I have computed (3483.34) is not among your choices.. so either I am wrong or your choices or given are wrong.
    Last edited by catenary; August 19th 2014 at 07:21 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member jonah's Avatar
    Joined
    Apr 2008
    Posts
    133
    Thanks
    9

    Re: Annuity Problem - deferred

    Quote Originally Posted by catenary View Post
    However the answer I have computed (3483.34) is not among your choices..
    It shouldn't be.
    Quote Originally Posted by catenary View Post
    so either I am wrong or your choices or given are wrong.
    The given is just fine.

    Accordingly, we have the following equation of value :

    100000=R*[1-(1.02)^(-30)]/.02*(1.02)^(-11)

    where R is the monthly payment.
    Last edited by topsquark; August 20th 2014 at 04:42 AM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member jonah's Avatar
    Joined
    Apr 2008
    Posts
    133
    Thanks
    9

    Re: Annuity Problem - deferred

    Quote Originally Posted by catenary View Post
    First you need to get what the cash balance would be 11 months from now using F = P(1 + i)^{(m*n)}. Then use the formula A = P*\dfrac{(\dfrac{r}{m})(1+\dfrac{r}{m})^{(m*n)}}{(  1+\dfrac{r}{m})^{(m*n)} - 1} where r is the nominal rate of interest which from your problem is 2%, n is the time in years, m is the number of times compounded in one year so in this case 12.
    Just out curiosity, how did you apply your formulas?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Feb 2014
    From
    Negros
    Posts
    110
    Thanks
    7

    Re: Annuity Problem - deferred

    Quote Originally Posted by jonah View Post
    Just out curiosity, how did you apply your formulas?
    Well neither does your equation seem to give a value among the choices..

    Here is how it is applied:
    F = 100000(1+\frac{.02}{12})^{12*\frac{11}{12}} = 101,848.6878 It is 11 months because we start computing the payment of the first annuity based off this which will be a month after the initial principal for which it is computed.
    Then,
     101,848.6878*\dfrac{(\frac{.02}{12})(1+\frac{.02}{  12})^{(12*2.5)}}{(1+\frac{.02}{12})^{(12*2.5)} - 1} = 3483.365176
    Last edited by catenary; August 19th 2014 at 12:00 PM.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member jonah's Avatar
    Joined
    Apr 2008
    Posts
    133
    Thanks
    9

    Re: Annuity Problem - deferred

    Quote Originally Posted by catenary View Post
    Well neither does your equation seem to give a value among the choices..
    Actually, it does. It really does. It's practically a dead giveaway to the OP minus the analysis of course. It's up to him or her to calculate the monthly payment as depicted in my equation of value. Since you were not able to come up with one of the choices using my equation

    Quote Originally Posted by catenary View Post
    Here is how it is applied:
    F = 100000(1+\frac{.02}{12})^{12*\frac{11}{12}} = 101,848.6878 It is 11 months because we start computing the payment of the first annuity based off this which will be a month after the initial principal for which it is computed.
    Then,
     101,848.6878*\dfrac{(\frac{.02}{12})(1+\frac{.02}{  12})^{(12*2.5)}}{(1+\frac{.02}{12})^{(12*2.5)} - 1} = 3483.365176
    Alas Sir catenary, I must object on how you misapplied the fundamental compound interest formula. You clearly (as far as my happy inebriated brain could tell) plugged in incorrect values. You may need a review of nominal and effective rates. And what about that other formula? Whoever gave you that formula must be out of his mind.

    Cheers.
    Last edited by topsquark; August 20th 2014 at 04:41 AM.
    Thanks from topsquark
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Aug 2014
    From
    Philippines
    Posts
    2

    Re: Annuity Problem - deferred

    The answer in book is "a", but I cannot come up with a correct solution. thanks for helping...
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Member jonah's Avatar
    Joined
    Apr 2008
    Posts
    133
    Thanks
    9

    Re: Annuity Problem - deferred

    Quote Originally Posted by lynyrdz View Post
    The answer in book is "a", but I cannot come up with a correct solution. thanks for helping...
    Is this post an indication that you already worked out the simple algebra of my equation of value (see my 1st post) to match your book.

    Come to think of it, I guess my 1st post was practically a spoon fed solution.
    Last edited by topsquark; August 20th 2014 at 04:40 AM.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Member
    Joined
    Feb 2014
    From
    Negros
    Posts
    110
    Thanks
    7

    Re: Annuity Problem - deferred

    I realize that I mistook the 2% stated in the problem to be the nominal rate of interest(r). Turns out it is actually the rate of interest per period(i). you can replace all of the \frac{r}{m} in the formula I gave with just 'i' now, because i = \frac{r}{m} and it now gives "a" from the choices.

    Im not certain, but I think that when interpreting interest problems, if you have a statement like "with 2% interest monthly" then it means that 2% is the rate of interest per period while the number of compounding periods in one year is 12, but if you have a statement like "with interest at 2% compounded monthly" then it means that 2% is the nominal rate of interest while the number of compounding periods is still 12. credits to sir jonah for nudging me towards this direction.
    Last edited by catenary; August 20th 2014 at 08:58 AM.
    Thanks from topsquark
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Super Member
    Joined
    Nov 2007
    From
    Trumbull Ct
    Posts
    914
    Thanks
    27

    Re: Annuity Problem - deferred

    compound amount after 1 year
    CA =100,000* (1+.02)^12 = 100,000* (1.268) = 126800
    capital recovery in 30 months =126800* (.02 ) (1.02)^30/(1.02)^30-1= 126800*(.0447)=5668 per month
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Member
    Joined
    Feb 2014
    From
    Negros
    Posts
    110
    Thanks
    7

    Re: Annuity Problem - deferred

    [deleted what I wrote, sorry for unintentionally bumping the thread; accident]
    Last edited by catenary; August 20th 2014 at 10:26 AM.
    Follow Math Help Forum on Facebook and Google+

  12. #12
    Member jonah's Avatar
    Joined
    Apr 2008
    Posts
    133
    Thanks
    9

    Re: Annuity Problem - deferred

    WARNING: Beer soaked rambling/opinion/observation ahead. Read at your own risk. Not to be taken seriously. In no event shall Sir jonah in his inebriated state be liable to anyone for special, collateral, incidental, or consequential damages in connection with or arising out of the use of his beer (and tequila) powered views.

    Quote Originally Posted by bjhopper View Post
    compound amount after 1 year
    CA =100,000* (1+.02)^12 = 100,000* (1.268) = 126800
    Must object to this intermediate rounding. We might as well use all the digits of a calculator's display (or stored value) to achieve the highest possible accuracy. Thus,
    100,000*(1+.02)^12=126,824.17945625... or 126,824.18
    Rounding to the nearest cent might be acceptable in some circles but shaving $24.18 is way too much rounding.
    Quote Originally Posted by bjhopper View Post
    capital recovery in 30 months =126800* (.02 ) (1.02)^30/(1.02)^30-1= 126800*(.0447)=5668 per month
    Not entirely sure what kind of grouping went on here but by WolframAlpha (go here),
    (.02 ) (1.02)^30/(1.02)^30-1 is definitely not equal to .0447

    Clearly, the end of one year was used as the comparison date.
    It should have been (using compound interest formula and annuity due version of the amortization formula)
    100000(1.02)^12=R*[1-(1.02)^(-30)]/.02*(1.02)
    Whatever comparison date you choose, be it the present, the end of 11 months, the end of 1 year, etc., the monthly payment will be always be the same.
    With the end of the 41st month (11 + 30) as comparison date, we would have
    100000(1.02)^41=R[(1.02)^30-1]/.02
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Deferred Annuity problem
    Posted in the Business Math Forum
    Replies: 18
    Last Post: May 19th 2014, 12:35 PM
  2. Pv: annuity problem
    Posted in the Business Math Forum
    Replies: 2
    Last Post: June 20th 2013, 12:12 AM
  3. Var[n-deferred whole life annuity-due]
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: March 26th 2011, 12:11 PM
  4. Replies: 2
    Last Post: March 30th 2010, 05:22 PM
  5. Deferred annuity problem
    Posted in the Algebra Forum
    Replies: 3
    Last Post: March 24th 2009, 12:14 PM

Search Tags


/mathhelpforum @mathhelpforum