Question

find the cash value of the lottery jackpot given below. Yearly jackpot payments begin immediatley ....

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) ____ ?.

Homework Answers

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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