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:

2 3 4 81 3 3 3 3 3 The total is simply given by

93 19841

3 1

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

log 1

log(1 )

FV iPMTn

i

It seems more reasonable to just solve this exponential equation in the usual way.

Does it Check?