Question 1209351
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A bank offers 5% compound interest calculated on half yearly basis. 
A customer {{{highlight(cross(deposit))}}} <U>deposits</U> 1600 each on 1st January and 1st July of a year. 
Find the interest it would have gained at the end of the year 
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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Formulation of the problem is a bit strange, &nbsp;since it does not concretizes

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;at the end of which year it wants to get the interest/answer.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;So, &nbsp;I will assume that it wants the interest at the end of the first year.



<pre>
It is an 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 semi-annual payment (deposit); 
r is the semi-annual effective rate presented as a decimal; 
n is the number of deposits (= the number of years multiplied by 2, in this case).


Under the given conditions, P = 1600;  r = 0.05/2 = 0.025;  n = 1*2 = 2.  
So, according to the formula (1), Future Value of the account at the end of the first year


    FV = {{{1600*(1+0.025)*(((1+0.025)^2-1)/0.025)}}} =  3321.


Note that the customer will deposit only  2*1600 = 3200 in two semi-annual payments.  
So, the interest at the end of the first year is  3321 - 3200 = 121.    <U>ANSWER</U>
</pre>

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

&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/Finance/Find-future-value-of-an-Annuity-Due-saving-plan.lesson>Find future value for an Annuity Due saving plan</A> 

in this site.


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