Question 1198671
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Suppose a state lottery prize of $3 million is to be paid in 25 payments of $120,000 each 
at the end of each of the next 25 years. If money is worth 11%, compounded annually, 
what is the present value of the prize? (Round your answer to the nearest cent.)
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We have a sinking fund.  Its initial value is unknown and we should find it - it is a present value of the fund.


We know that the initial money is deposited for 25 years at 11% annual rate, 
paid out $120,000 and compounded (both) at the end of each year.


Use the formula for the present value of such sinking fund


    PV = {{{PMT*((1 - (1+r)^(-n))/r)}}},


where PV is the present value, PMT is the annual payment value, 
r is the annual rate, n is the number of payment/compounding (the number of years, in this problem).


With the given data, the formula for calculations is


    PV = {{{120000*((1-(1+0.11)^(-25))/0.11)}}} = {{{120000*((1-1.11^(-25))/0.11)}}} = 1,010,609.36  dollars.



<U>ANSWER</U>.  The present value of the prize is  $1,010,609.36.

         This amount should be deposited initially, and it will provide
         no-failure payments of $120,000 at the end of each year during 25 years,
         under given conditions.
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Solved.