Question 1194566
.
You deposit $3000 at the beginning of each year into an account earning 6% interest 
compounded annually. How much will you have in the account in 20 years?
~~~~~~~~~~~~~~~


<pre>
It is a classic Annuity Due saving plan. The general formula is 


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


where  FV is the future value of the account;  P is the annual payment (deposit); 
r is the annual percentage rate presented as a decimal; 
n is the number of deposits (= the number of years, in this case).


Under the given conditions, P = 3000;  r = 0.06;  n = 20.  So, according to the formula (1), you get at the end of the 20-th year


    FV = {{{3000*(((1+0.06)^20-1)/0.06)}}} = $110,356.77.


Note that you deposit only  20*$3000 = $60,000.  The rest is the interest which the account earns/accumulates in 20 years.
</pre>

-----------------


On Ordinary Annuity saving plans and Annuity Due 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=http://www.algebra.com/algebra/homework/Sequences-and-series/Annuity-due-saving-plans-and-geometric-progressions.lesson>Annuity Due 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>

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.