Question 1164749
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Determine the present value of a series of 60 monthly payments of $2,500 each which begins 1 month from today. 
Assume interest of 10 percent per year compounded quarterly.
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In this tricky problem, the monthly payments are not compounded. 


Monthly payments lie in the bank and wait for the end of a quarter - 
only then they are compounded, according to the problem.


So, we actually have quarterly payments of 3*2500 = 7500 dollars each, compounded quarterly.


Thus, it works as an Ordinary Annuity saving plan with quarterly payments of $7500 
at the end of each quarter, compounded quarterly at the annual rate of 10%.


60 monthly payments of $2500 each mean 60/3 = 20 quarterly payments of $7500 each.


So, the future value of the account after 20 quarters will be

    FV = {{{7500*(((1+0.1/4)^20-1)/((0.1/4)))}}} = 191584.93  dollars.


Now we want to find the present value X.  It is the starting value of the account,
which, when compounded quarterly at 10% per year, will have the same future value in 20 quarters.


So, we write this equation

    191584.93 = {{{X*(1+0.1/4)^20}}}.


It gives the solution

    X = {{{191584.93/(1+0.1/4)^20}}} = 116918.72  dollars.


<U>ANSWER</U>.  The present value is $116918.72 dollars.
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Solved.