You won the lottery. You have two options for your payment. In option $1,$ you are going to receive $$10,000$ now. In option $2,$ you receive $$1,100$ every year for $12$ years, where the first payment is made today $($annuity due$).$ If the interest rate is $6\%,$ what is your choice? What is your choice if the interest rate is $5\%$ instead?

Question $11$ options:

Option $1$ at both $6\%$ and $5\%$ rate

You are indifferent between the two options

Option $1$ at $6\%$ rate and Option $2$ at $5\%$ rate

Option $2$ at both $6\%$ and $5\%$ rate