Question

find the cash value of the lottery jackpot given below. Yearly
jackpot payments begin immediatley . assume the lottery can invest
at the given intrest rate.

$16,000,000 jackpot, 7% interest, 20 annual payments

jackpot amount $16,000,000

interest rate 7%

equal annual payments 20

present value (in dollar) ____ ?.

Answer #1

As the payments begin immediately then this is the case of an annuity due.

Here PMT = 16,000,000

r = 7% and n = 20

Thus present value can be computed using the "PV" function in excel. The syntax will be:

PV(7%, 20, -16000000,,1)

**= $181,369,523.88. This can be rounded to
$181,369,524**

Alternatively we can use the formula: Present Value of Annuity Due = PMT + PMT x ((1 - (1 + r) ^ -(n-1) / r)

= 16,000,000 + 16,000,000*((1-(1+7%)^-(20-1)/7%)

= 16,000,000+16,000,000*(1-1.07^-(19)/0.07)

=16,000,000+(16,000,000*10.3356)

= 16,000,000+165,369,523.88

= $181,369,523.88

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$
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$
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$
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