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# Determining the present value of an investment at a set rate

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In May 1992, a 60 yr old nurse gambled \$12 in a Reno casino and walked away with the biggest jackpot in history - \$9.3 million. In reality, the jackpot wasn't really worth \$9.3 million. The sum was to be paid in 20 annual installments of \$465,000 each. What is the present value of the jackpot?

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The present value of these payments is simply the sum of the present values of each payment. But rather than valuing each payment separately, it is much easier to treat the cash payments as a 20 year annuity. To value this annuity we simply multiply \$465,000 by the 20 year annuity factor:
PV = \$465,000 X 20 year annuity factor
= \$465,000 X (1/r - 1/r(1+r)^20)

At an interest rate of 8%, the annuity factor is:

(1/.08 - 1/.08(1.08)^20) = 9.818.

note: ^ refers to "the power of"

The present value of the \$465,000 annuity is \$465,000 X 9.818 = \$4,565,000. The \$9.3 prize has a true value of approx \$4.6 million.

The present value is the price which investors would be prepared to offer for the series of cash flows.

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