Question 1172999
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At what rate, compounded monthly should P25,000 be deposited in a bank to gain an interest of P4,500 in 3 years?
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            It is one of the typical problems on periodically compounded account, 
            but slightly changed/modified comparing with traditional formulation.


            So,  my first step is  to convert  the problem to its traditional form.


            To convert it,  notice that having the principal of  P25,000   and gaining the interest of  P4,500 

            MEANS  that the  Future  Value  is   P25,000 + P4,500 = P29,500.


            So,  now we have this traditional formulation


<pre>
           +----------------------------------------------------------------+
           |   Find the nominal annual rate at which the principal P25,000  |
           |   compounded monthly becomes P29,500 in 3 years ?              |
           +----------------------------------------------------------------+
</pre>


Now this standard problem is &nbsp;EASY &nbsp;to &nbsp;SOLVE.



<pre>
    29500 = {{{25000*(1+r/12)^(3*12)}}}


    {{{29500/25000}}} = {{{(1+r/12)^36}}}


    {{{(1+r/12)^36}}} = 1.18


    {{{log(10,(1 + r/12))}}} = {{{(1/36)*log(10,(1.18))}}} = 0.001997

    {{{1 + r/12}}}  = {{{10^0.001997}}} = 1.004609.

      {{{r/12}}}    = 1.004609 - 1 = 0.004609

        r    = 12*0.004609 = 0.055308 = 0.055 (rounded) = 5.5%.    <U>ANSWER</U>


<U>CHECK</U>.  {{{25000*(1+0.055308/12)^(3*12)}}} = 29500.84.   Good enough.
</pre>

Solved.