Answer each of the following independent questions.

You recently won a lottery and have the option of receiving one of the following three prizes: $(1)$ $$76,000$ cash immediately, $(2)$ $$27,000$ cash immediately and a six$-$year annual annuity of $$8,500$ beginning one year from today, or $(3)$ a six$-$year annual annuity of $$15,800$ 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 $$145,000$ 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?

Note: Use tables, Excel, or a financial calculator. $($FV of $$1,$ PV of $$1,$ FVA of $$1,$ PVA of $$1,$ FVAD of $$1$ and PVAD of $$1)$

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You recently won a lottery and have the option of receiving one of the following three prizes: $(1)$ $$76,000$ cash immediately, $(2)$ $$27,000$ cash immediately and a six$-$year annual annuity of $$8,500$ beginning one year from today, or $(3)$ a six$-$year annual annuity of $$15,800$ 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?

Note: Round your final answers to nearest whole dollar amount.

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