A $3.6 million state lottery pays $15,000 at the beginning of each month for 20 years. How much money must the state actually have in hand to set up the payments for this prize if money is worth 5.8%, compounded monthly

Present Value= $2,128,538.66

Explanation:

Giving the following information:

Cash flow= $15,000

Number of periods= 20*12= 240

Interest rate= 0.058/12= 0.00483

First, we need to calculate the future value of the monthly payments:

FV= {A*[(1+i)^n-1]}/i

A= monthly deposit

FV={15,000*[(1.00483^240) - 1]} / 0.00483

FV= $6,765,529.2

Now, the present value:

PV= FV/(1+i)^n

PV= 6,765,529.2 / 1.00483^240

PV= $2,128,538.66

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