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annuity question from the finan manual

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  • annuity question from the finan manual

    here is the question:

    An annuity pays 100 at the end of each month for 20 years. Using a nominal rate of interest of 4% compounded quarterly, calculate the current value of the annuity at the end of the 3rd year.

    Ok, so I found a present value of 16,521.23 (calculated a monthly interest rate of.33222835%)

    Now, in my understanding, to find the current value of the annuity at the end of the 3rd year, you would take the present value of the remaining payments (in this case, 204). The correct answer is $18,616.53, which is what you get when you take 16,521.23 and multiply it by (1.0033222835^36).

    Why is this the answer? Doesn't the value of the annuity decrease as each payment is made, eventually becoming zero when the last payment is made? Or do I have it backwards?
    Exams Passed:

    P FM

  • #2
    the future value should be greater than the present value as long as the interest rate is positive because PV * (1 + i)^n = FV

    How many payment is made does not affect the total value of the annuity.

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    • #3
      Originally posted by BeanCounter View Post
      the future value should be greater than the present value as long as the interest rate is positive because PV * (1 + i)^n = FV

      How many payment is made does not affect the total value of the annuity.
      Im still confused, sorry. To me, i understood it that an annuity works the same way as a loan. (I purchase the annuity, I pay 16,521.33 for it now and they pay me back by paying me 100 at the end of each month for 20 years). Then, shouldn't the value of the annuity go DOWN as payments are made? There are only 204 payments left after 3 years, as opposed to 240 at the beginning. What am I missing?
      Exams Passed:

      P FM

      Comment


      • #4
        Originally posted by MisterMoa View Post
        Im still confused, sorry. To me, i understood it that an annuity works the same way as a loan. (I purchase the annuity, I pay 16,521.33 for it now and they pay me back by paying me 100 at the end of each month for 20 years). Then, shouldn't the value of the annuity go DOWN as payments are made? There are only 204 payments left after 3 years, as opposed to 240 at the beginning. What am I missing?
        Got it figured out. I am getting caught up on the wording. I assumed it meant, what is the value after three years, in which case my method here is correct. "Current" value means to take the present value and basically find the future value after three years.
        Exams Passed:

        P FM

        Comment


        • #5
          Yes, I think you mixed up balance and value.

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