Question 1186136
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A new mother would like to start a college fund for her newborn daughter. She makes quarterly deposits 
of $500 into a college fund that earns 6% compounded quarterly for the next 18 years.
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How much will her daughter have available in her college fund when she turns 18? $
Round to the nearest dollar
What is total amount the mother deposited into the fund over the 18 years? $
Round to the nearest dollar
How much interest was earned over the 18 years? $
Round to the nearest dollar
Use the WHOLE DOLLAR AMOUNTS you entered in as your answers above.
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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 the quarterly payment (deposit); 
r is the quarterly effective percentage yield presented as a decimal; 
n is the number of deposits (= the number of years multiplied by 4, in this case).


Under the given conditions, P = 500;  r = 0.06/4;  n = 4*18 = 72.  
So, according to the formula (1), she will get at the end of the 18-th year


    FV = {{{500*(((1+0.06/4)^(4*18)-1)/((0.06/4)))}}} = {{{500*((1.015^72-1)/0.015)}}} = $64038   (rounded).


Note that she will deposit only  4*18*$500 = $36,000.  The rest is what the account earns/accumulates in 18 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>

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.