Answer each of the following independent questions.

You recently won a lottery and have the option of receiving one of the following three prizes: $(1)$ $$64,000$ cash immediately, $(2)$ $$21,000$ cash immediately and a six$-$year annual annuity of $$7,700$ beginning one year from today, or $(3)$ a six$-$year annual annuity of $$13,300$ beginning one year from today. Assuming an interest rate of $7\%$ compounded annually, determine the present value for the above options. Which option should you choose?

A company wants to accumulate a sum of money to repay certain debts due in the future. The company will make annual deposits of $$115,000$ into a special bank account at the end of each of $10$ years. Assuming the bank account pays $8\%$ interest compounded annually, what will be the fund balance after the last payment is made in ten years?