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Annuities – the “Future Value”of periodic deposits
Mat 112
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First, a note
To compute a particular type of sum (a “geometric sum”), where the terms are powers of some number, such as:
2 3 4 81 3 3 3 3 3 The total is simply given by
93 19841
3 1
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Annuities
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Forming a “future value”
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Making Deposits
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First Deposit
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Second Deposit
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And so on…
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…for a total of ?
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Interest Earned?
$2501.51 ($200.00 12) $101.51
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Future Value formula
Why? Results from determining the geometric sum.
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Given FV, find PMT
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FV formula
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Examples for Future Value
Mat 112
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FV Example
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How much interest?
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PMT Example
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Calculate carefully!
PMT = $104.31 (or round up to $104.32 to be safe)
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Example: “quarterly deposits”
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Example: “IRA”
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Solving for n?
Mat 112
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A Bigger Challenge?
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Using the Log…
Or simply,
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Bring down the exponent
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Not Another Formula?
Although the text offers this result as a new formula and we could memorize
log 1
log(1 )
FV iPMTn
i
It seems more reasonable to just solve this exponential equation in the usual way.
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Does it Check?