Question 1207413
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Clark's younger brother saved $18 per month from his paper route for the past two years. 
If interest is 4% compounded quarterly, how much will he have accumulated in his savings account?
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<pre>
It is equivalently to say that Clark deposits 18*3 = 54 dollars at the end of every quarter 
into the ordinary annuity, which provides 4% annually compounded quarterly.


So, apply the general formula for ordinary annuity future value


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


where  FV is the future value of the annuity;  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 = 18*3 = 54 dollars;  r = 0.04/4 = 0.01;  n = 2*4 = 8.  
So, according to the formula (1), Clark's younger brother will get at the end of the 2-nd year


    FV = {{{54*(((1+0.01)^(2*4)-1)/0.01))}}} =  447.43  dollars  (rounded to the closest cent).
</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>

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