A man can sell his business for $$700,000$ cash or for $$100,000$ plus $$123,000$ at the end of each year for $9$ years.

a$.$ Find the present value of the annuity that is offered if money is worth $10\%,$ compounded annually.

b$.$ If he takes the $$700,000,$ spends $$100,000$ of it$,$ and invests the rest in a $9-$year annuity at $10\%,$ compounded annually, what size annuity payment will he receive at the end of each year?

c$.$ Which is better, taking the $$100,000$ and the annuity or taking the cash settlement?