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31 March, 05:19

You have just won the lottery and you will receive 10 annual beginning-of-year payments of $5 million each. If you expect to earn a 9% compounded semi-annually, what will be the current value of the lottery payments?

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  1. 31 March, 07:11
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    Current value of lottery=$ 33,983,233.98

    Explanation:

    The value of the lottery is the Present of the annual cash flow discovered at the discount rate of 9% compounded semi annually.

    Semi-annual rate = 9%/2 = 4.5%

    PV = A * (1 - (1+r) ^ (-n) / r

    A - 5,000,000/2 = 2,500,000. r - 4.5%, n - 2 * 10 = 20

    The first payment is already in its present value term, hence it is already discounted.

    The balance of 19 payments would be discounted as follows

    PV = 2,500,000 * (1 - (1.045) ^ (-19) / 0.045

    = 31,483,233.98

    Current value of lottery = 2,500,000 + 31,483,233.98

    =$ 33,983,233.98
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