Lottery: Todd actually took his winnings as a one-time lump-sum payout of $30 million instead of the annual installments. What discount factor did the state of California use the arrive at $30 million as the present value?

The question is incomplete, so I looked for a similar one that can be used as an example (see attached image):

In this example, you are offered 30 annual payments, starting today, = $85,000,000 / 30 = $2,833,333 per year

in order to determine the present value of this annuity due:

present value = annual payment x PV annuity due factor

present value = $2,833,333 x 12.81039 (PV annuity due factor, 30 period, 7.5%) = $36,296,100

if you were given the present value and the annual payment, then you would need to determine the PV annuity factor:

PV annuity factor = present value / annual payment = $36,296,100 / $2,833,333 = 12.81039

to determine the interest rate we must use the following formula:

PV annuity due = ($1/i) · (1 + i) · {1 - [1 / (1 + i)ⁿ]}

12.81039 = ($1/i) · (1 + i) · {1 - [1 / (1 + i)³⁰]}

another way to figure it out is using annuity tables or calculators:

you know the annuity due factor = 12.81039 and the number of periods = 30, so you look down to see which interest rate matches them.

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