Question 1146477
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Jenny puts aside $20 at the end of each month for 3 years. How much will she have then of the investment earns 
8.2% p.a., paid monthly?
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        This my post is written in opposite to the solution by @mananth in his post.


        This Finance problem assumes a precise solution,  correct  to a single cent.



<pre>
Use a standard formula for a Future value of an ordinary annuity 


    FV = {{{PMT*((1+r/12)^(3*12)-1)/((r/12))}}} = {{{20*((1+0.082/12)^36-1)/((0.082/12))}}} = 813.16 dollars.   <U>ANSWER</U>
</pre>


Solved. &nbsp;&nbsp;In opposite to the answer in the post by @mananth, &nbsp;my answer is precise to one single cent.



To get a precise solution, &nbsp;use &nbsp;MS &nbsp;Excel spreadsheets or &nbsp;Google spreadsheet.
Write the formula in any text editor with the numbers and then copy-paste it into a spreadsheet cell &nbsp;" as is ".



You will get a precise answer with the precision, which is usually enough for 
normal/regular financial calculations, without intermediate rounding.


Another, alternative way, is to use specialized financial online calculators.
Many of them, often free of charge and  many-times repeatedly tested, can be found in the Internet
using appropriate key words for search, for example "online calculator future value of an annuity".



Below are the links to some popular web-sites with reliable online calculators 


https://www.calculatorsoup.com/calculators/financial/future-value-annuity-calculator.php


https://www.calculator.net/annuity-calculator.html


https://www.omnicalculator.com/finance/annuity-future-value



In this concrete calculations, &nbsp;I used &nbsp;MS &nbsp;Excel in my computer.



Happy calculations with reliable tools !