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Annuities –
the “Future Value”
of periodic deposits
Mat 112
First, a note
To compute a particular type of sum
(a “geometric sum”), where the terms are powers
of some number, such as:
1 3  3  3  3 
2
3
4
The total is simply given by
3 1
9
3 1
 9841
3
8
Annuities
Forming a “future value”
Making Deposits
First Deposit
Second Deposit
And so on…
…for a total of ?
Interest Earned?
$2501.51  ($200.00  12)  $101.51
Future Value formula
Why? Results from determining the geometric sum.
Given FV, find PMT
FV formula
Examples for
Future Value
Mat 112
FV Example
How much interest?
PMT Example
Calculate carefully!
PMT = $104.31
(or round up to $104.32 to be safe)
Example: “quarterly deposits”
Example: “IRA”
Solving for n?
Mat 112
A Bigger Challenge?
Using the Log…
Or simply,
Bring down the exponent
Not Another Formula?
Although the text offers this result as a new
formula and we could memorize
 FV  i

log 
 1
 PM T

n
log(1  i )
It seems more reasonable to just solve this
exponential equation in the usual way.
Does it Check?
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