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On his way home from work, Bill Harris was listening to the radio, which reminded him of the large Lotto Jackpot that night. So, Bill bought a ticket and won the jackpot of $50 million. Bill will be paid in 20 annual installments of $2.5 million. If Bill had selected the "cash value option", and the prevailing interest rate was 6%, his lump-sum payment would be: (Hint, present value of $2.5 million over 20 periods, using a 6% rate)

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Answer:

Ans. His payment would be $28,674,803.05

Explanation:

Hi, we just need to bring all the annual payments to present value, discounted at a 6% rate, for 20 years. The equation and the present value as follows.

[tex]Present Value=\frac{A((1+r)^{n}-1) }{r(1+r)^{n} }[/tex]

[tex]Present Value=\frac{2500000((1+0.06)^{20}-1) }{0.06(1+0.06)^{20} } =28674803.05[/tex]

Best of luck.

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