Question 1198726
.
Jimmy wants to save $2000 in 3 years for a down payment on a motorcycle. 
If he can earn 4% compounded quarterly, how much will he need to deposit 
each quarter in order to save this amount?
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<pre>
It is a classic Ordinary Annuity saving plan. The general formula is 


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


where  FV is the future value of the account;  P is the quarterly payment (deposit); 
       r is the effective quarterly rate presented as a decimal; 
       n is the number of deposits (= the number of years multiplied by 4, in this case).


From this formula, you get for the quarterly payment 


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


Under the given conditions, FV = $2,000;  r = 0.04/4 = 0.01;  n = 3*4 = 12.  
So, according to the formula (1), you get for the quarterly payment 


    P = {{{2000*(0.01/(1.01^12-1))}}} = $157.70.


<U>Answer</U>.  The necessary quartely deposit is $157.70.
</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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When you learn from these lessons, &nbsp;you will be able to do similar calculations in semi-automatic mode.