Question 1207539
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In order to accumulate enough money for a down payment on a​ house, a couple deposits 
$245 per month into an account paying 3 % compounded monthly. If payments are made 
at the end of each​ period, how much money will be in the account in 7 ​years?
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<pre>
It is a classic Ordinary Annuity saving plan. The general formula is 


    FV = {{{P*(((1+r)^n-1)/r)}}},    (1)


where  FV is the future value of the account;  P is your monthly payment (deposit); 
r is the monthly percentage yield presented as a decimal; 
n is the number of deposits (= the number of years multiplied by 12, in this case).


Under the given conditions, P = 245;  r = 0.03/12;  n = 12*7 = 84.  
So, according to the formula (1), the couple will get at the end of the 7-th year


    FV = {{{245*(((1+0.03/12)^(12*7)-1)/((0.03/12)))}}} = {{{245*(((1+0.03/12)^84-1)/((0.03/12)))}}} = 22868.77.


Round it to the closest dollar, get the <U>ANSWER</U>: In 7 years, about 22,869 dollars will be in the account.


Note that the couple deposits only  12*7*$245 = $20,580.  The rest is what the account earns/accumulates in 7 years.
</pre>

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On Ordinary Annuity saving plans, &nbsp;see the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Ordinary-Annuity-saving-plans-and-geometric-progressions.lesson>Ordinary Annuity saving plans and geometric progressions</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Sequences-and-series/Solved-problem-on-Ordinary-Annuity-saving-plans.lesson>Solved problems on Ordinary Annuity saving plans</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Finance/Find-future-value-of-an-Ordinary-Annuity.lesson>Find future value of an Ordinary Annuity</A>

in this site.


The lessons contain &nbsp;EVERYTHING &nbsp;you need to know about this subject, &nbsp;in clear and compact form.


When you learn from these lessons, &nbsp;you will be able to do similar calculations in semi-automatic mode.