Results 1 to 12 of 12

Math Help - Deferred Annuity problem

  1. #1
    Newbie
    Joined
    May 2012
    From
    Home
    Posts
    1

    Deferred Annuity problem

    I need help answering this problem:

    A sequence of 8 annual payments of $750 each, with the first payment due at the beginning of the 6th year; money is worth 6%. (The beginning of year 6 is the end of year 5.) Find the present value.

    This is my answer: 750 [ (1-1.06^-13) / .06 ] - 750 [ (1-1.06^-5) / .06 ] = $3,480.24

    and this is the book's: $3,689 .

    The book didn't provide a solution, so I would really appreciate it if someone can help me find where my solution went wrong. Thank you!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Feb 2011
    Posts
    20

    Re: Deferred Annuity problem

    I think the book just had an error, your answer is correct by using the Annuity PV formula for years 13 and 5 and taking one away from the other
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Mar 2010
    From
    Mumbai
    Posts
    91
    Thanks
    2

    Re: Deferred Annuity problem

    the book has correct answer.

    Firstly why did u take 750 when the payment is 575.82 ?
    Secondly if you are taking 13 and 5 it says that your payments are made in advance, but the formula you used is for payments being made at the end. If you wanna use this formula only then you must take 12 and 4.

    here i attached what i did Deferred Annuity problem-dscn1067.jpg did gave an answer 2,834.31€
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Feb 2011
    Posts
    20

    Re: Deferred Annuity problem

    Why would you use 575.82? Since its an annuity problem you use the actual value of the payments, not discounted value since the formula discounts the payment for you. The payments are made in years 6 and 14 so we use the end of year 5 and 13. This is also correct.

    The answer you gave at the end is about 800 too low.... so it is not correct.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Mar 2010
    From
    Mumbai
    Posts
    91
    Thanks
    2

    Re: Deferred Annuity problem

    I'm not getting you, the problem clearly says that the payments are 575.82 so, why would you take 750?
    And the first payment is at the beginning of 6th year which is end of 5th year. If you are considering 5 and 13 that says you have 5 years which have no payment at the beginning of each year and 8 years with a payment of 575.82 at the beginning of each year.

    you are using this right \frac {1-1.06^{-n}}{0.06}, but this will work when your payments are made at the end of each year (i.e., by taking 4 and 12).

    Use \frac {1-1.06^{-n}} {\frac {0.06}{1.06}}, when payments are made in advance (i.e., by taking 5 and 13).

    Either of them will give you correct answer with payment 575.82 not 750.

    check this in wolframalpha:

    575.82 [ (1-1.06^(-13)) /( .06/1.06) ] - 575.82 [ (1-1.06^(-5)) / (.06/1.06) ] - Wolfram|Alpha
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Feb 2011
    Posts
    20

    Re: Deferred Annuity problem

    I'm not getting you either, where did you get the 575.82? The OP clearly stated the payments are 750. Also the reason we use years 5 and 13 is because beginning of the 6th year = end of 5th year, why would you have to go back 1 year more?

    Also since the answer you have given is clearly not the same as that of the text book, your answer is obvious not correct either. Stop trolling
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member
    Joined
    Mar 2010
    From
    Mumbai
    Posts
    91
    Thanks
    2

    Re: Deferred Annuity problem

    Ok my bad.
    But just change the payment from 575.82 to 750 gives me the answer as 3689 which is the exact. You can check.

    NB: in my browser it shows me the payments in euros, that's why i have taken 575.82 yesterday.
    Last edited by amul28; May 9th 2012 at 06:48 PM.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor
    Joined
    Dec 2007
    From
    Ottawa, Canada
    Posts
    3,069
    Thanks
    65

    Re: Deferred Annuity problem

    Why don't you look at it this way:
    at end of year 4, a loan is set up at 8 payments of $750, rate 6%; 1st payment end of year 5:
    that'll give you a present value (loan proceeds) of $4,657.
    Now just get present value of that today: 4657 / 1.06^4 = 3689
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Member
    Joined
    Mar 2010
    From
    Mumbai
    Posts
    91
    Thanks
    2

    Re: Deferred Annuity problem

    My attachment shows this method, except for the payments.
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Senior Member
    Joined
    Oct 2009
    Posts
    295
    Thanks
    9

    Re: Deferred Annuity problem

    It looks like you're using the formula for an annuity immediate (when interest is applied at the end of the year), rather than for an annuity due (when interest is applied at the beginning of the year).

    The formula should be

    \"{a}_{n,i}=\frac{1-\frac{1}{1+i}^{n}}{\frac{i}{1+i}}

    So, what you typed should look like this:

    750 [[ (1-1.06^-13) / .06 ]/1.06] - 750 [[ (1-1.06^-5) / .06 ]/1.06]=3,689.0544

    I hope that helps.
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Newbie
    Joined
    Nov 2013
    From
    NYC
    Posts
    2

    Re: Deferred Annuity problem

    I took a different approach to a solution:
    I used Excel and created a simple timeline of 12 periods, populating zero into the first four, and 750 in periods five through twelve, thus representing four time-periods with zero payments, followed by eight with $750.

    I then used the NPV function with a 6% rate, and the stream of cash flows (Note: with the first 750 entered in period 5, this is assuming payment at the END of the 5th period {or the beginning of #6})

    The NPV evaluates to $3,689.05; the same as the text book.

    To Amul28's comment about Euros vs Dollars, it wouldn't matter as long as the same units are used throughout...
    Follow Math Help Forum on Facebook and Google+

  12. #12
    Newbie
    Joined
    Nov 2013
    From
    NYC
    Posts
    2

    Re: Deferred Annuity problem

    FYI, copying and pasting that formula into Wolfram Alpha results in a valuation of 3,283.24

    Quote Originally Posted by downthesun01 View Post
    The formula should be

    \"{a}_{n,i}=\frac{1-\frac{1}{1+i}^{n}}{\frac{i}{1+i}}

    So, what you typed should look like this:

    750 [[ (1-1.06^-13) / .06 ]/1.06] - 750 [[ (1-1.06^-5) / .06 ]/1.06]=3,689.0544
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Var[n-deferred whole life annuity-due]
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: March 26th 2011, 12:11 PM
  2. Replies: 2
    Last Post: March 30th 2010, 05:22 PM
  3. Another annuity problem?
    Posted in the Business Math Forum
    Replies: 5
    Last Post: July 22nd 2009, 04:11 AM
  4. Deferred annuity problem
    Posted in the Algebra Forum
    Replies: 3
    Last Post: March 24th 2009, 12:14 PM
  5. Annuity Due Problem
    Posted in the Business Math Forum
    Replies: 0
    Last Post: March 4th 2009, 08:56 PM

Search Tags


/mathhelpforum @mathhelpforum