SOLUTION: 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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Question 1164749: 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.
Answer by ikleyn(52767)   (Show Source): You can put this solution on YOUR website!
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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 =  = 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 = .


It gives the solution

    X =  = 116918.72  dollars.


ANSWER.  The present value is $116918.72 dollars.

Solved.



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