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need help with basic annuities question.

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  • need help with basic annuities question.

    Here is the question:

    A loan of $12,000 is to be repaid within one yr. with level monthly payments, due at the beginning of of each month.

    The 12 payments equal $1000 each.
    A finance charge of $632 is also due with the first payment.

    Calculate the effective annual interest rate of the loan?

    here's what I come up with:

    12000 = (1000 + 632) + 1000 (a'') 11 | i

    the equation they have is: (correct one)

    12000 = (1000+632) + 1000 a 11 | i

    they are saying in the problem that the payment is due at the beginning of each month, therefore it suppose to be annunity-Due, but somehow they are using annuity immediate.

    Any idea why, please explain.

    Thanks!

  • #2
    Originally posted by sm9764
    Here is the question:

    A loan of $12,000 is to be repaid within one yr. with level monthly payments, due at the beginning of of each month.

    The 12 payments equal $1000 each.
    A finance charge of $632 is also due with the first payment.

    Calculate the effective annual interest rate of the loan?

    here's what I come up with:

    12000 = (1000 + 632) + 1000 (a'') 11 | i

    the equation they have is: (correct one)

    12000 = (1000+632) + 1000 a 11 | i

    they are saying in the problem that the payment is due at the beginning of each month, therefore it suppose to be annunity-Due, but somehow they are using annuity immediate.

    Any idea why, please explain.

    Thanks!
    Because you already have the first payment, which is $1,632. All subsequent payments begin coming once a month, starting one month later, which means that their present value would then be calculated like an annuity-immediate.

    If you wanted to use the annuity due formula, the formula should look like:

    12000 = 632 + 1000 (a'') 12| i

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    • #3
      question about the previous thread

      Yes, it makes perfect sense now. but somehow the answer does not match with the book answer.

      Ans: 12.7%

      any idea?

      Comment


      • #4
        Originally posted by sm9764
        Yes, it makes perfect sense now. but somehow the answer does not match with the book answer.

        Ans: 12.7%

        any idea?
        I mistakenly put i in the denominator when it should have been d. That might be the problem

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        • #5
          Oh, and what you might be getting is the monthly interest rate- I forgot to convert that to effective annual the first time I tried it. Monthly interest is0.999386%, which converted annually is 12.674%.

          Comment


          • #6
            yep! that's it... I tried to convert it by using effective rate interest formula, got some off value. Can you post the method you used.

            Thanks!
            Last edited by sm9764; October 23 2005, 09:54 PM.

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            • #7
              I just did 1.00999386^12.

              Comment


              • #8
                Yeah, I forgot dividing .999386/100. Thanks man..

                Comment


                • #9
                  You guys should really be using your calculator. It makes life much easier.
                  PV = -(12000-632)
                  2nd beginning of year payments
                  pmt = 1000
                  n = 12
                  12P/Y
                  1 C/Y
                  and you get i = 12.674%.
                  Whether you are the lion or the gazelle, when the sun comes up, you better be running.

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