You are offered to buy a lottery that has three tiers of prize. The jackpot gives you $10,000 with 0.1% chance; the good tier gives you $100 with 0.9% chance; and the okay tier gives you $5 with 99% chance. You have a log utility function U=ln(w)U=ln(w) where ww is your wealth. Assume you currently don't have any other wealth. How much are you willing to pay for this lottery? That is, what is the certainty equivalence of this lottery. (Fill in a number with 2 decimal points.)

Hint: The probabilistically/actuarially fair price of this lottery is:

100000.1%+1000.9%+599%=15.85100000.1%+1000.9%+599%=15.85

This is not what this question is asking.