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Math Help - Simple Annuity calculation

  1. #1
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    Simple Annuity calculation

    Hi,

    I'm having a problem comng up with an answer to a certain question regarding a simple annuity. The question says a person wants to accumulate $50,000 by the end of 10 years, making payments at the end of each month for the first six, then doubling the payments for the rermaining four years. The question wants to know what the size of the payments will be if interest is calculated at 12% per year.

    I tried adding together the two sections like this:

    50000 = PMT{ ((1 + 0.01)^72 - 1) / 0.01 } + 2*PMT{ ((1 + 0.01)^48 - 1) / 0.01 }

    which gave me the wrong answer.

    Any help is appreciated, thanks in advance.
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  2. #2
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    You have created two separate payment streams starting at the beginning of the 10 years. The first is accumulated 72 months - and then stops. The second 48 months.

    Look how slightly different the correct solution is, then ponder what I said:

    50000 = PMT{ ((1 + 0.01)^72 - 1) / 0.01 }*(1 + 0.01)^48 + 2*PMT{ ((1 + 0.01)^48 - 1) / 0.01 }
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  3. #3
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    Thanks for responding. OK, it worked, but why wouldn't you put the same extra bit at the end of the second part as well? I'm looking at some textbook examples for a similar problem that has the extra factor multiplied on to both portions and it's just not getting through my brain.
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  4. #4
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    Two ways to ponder it:

    1a) Accumulate for 72 months while paying PMT and then 48 months without making payments.

    then add

    1b) Accumulate 48 months while paying 2*PMT. There is no accumulation without payments

    2a) Accumulate 120 months while paying PMT.

    then add

    2b) Accumulate 48 months while paying PMT.

    Compare and contract these two styles. They have the some solution.

    Really, if you learn to draw it with Basic Principles, you will not EVER be confused. If you MUST use the formulas, you will have little recourse when confusion confronts you.
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