Question 1198080
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The periodic payments PMT necessary to accumulate the given amount in an annuity account. 
(Assume end-of-period deposits and compounding at the same intervals as deposits). 
$50,000 in a fund paying 5% per year, with monthly payments for 5 years, if the fund contains $10,000 at the start.
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<pre>
Let solve the problem in 2 steps.


                           <U>Step 1</U>


The future value of the initial amount of $10,000 in 5 years will be

    {{{10000*(1+0.05/12)^(5*12)}}} = {{{10000*(1+0.05/12)^60}}} = 12,833.59 dollars.


Thus, making monthly deposits of X dollars, we should accrue  the rest  50000 - 12833.59 = 37166.41 dollars in 5 years,
with compounding.


                           <U>Step 2</U>


Now we write the future value equation for an ordinary annuity with the monthly deposits of X dollars,
compounded monthly at 5% annual interest


    {{{X*(((1+0.05/12)^(5*12)-1)/((0.05/12)))}}} = 37166.41,


We calculate the factor/multiplier at X separately, and we get this equation


    X*68.00608284 = 37166.41.


Solve for X and get the <U>ANSWER</U>


    X = {{{37166.41/68.00608284}}} = 546.52.


At this point, the problem is solved completely.


The necessary monthly deposit is  546.52 dollars.
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Hip-hip, hurray !