SOLUTION: 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

Question 1198671: 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.)

Answer by ikleyn(52776) (Show Source): You can put this solution on YOUR website!
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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.)
~~~~~~~~~~~~~~~~~~~~~~

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 = ,


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 =  =  = 1,010,609.36  dollars.



ANSWER.  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.

Solved.

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