$(10$ points$)$ Eichelberger Trucking won a settlement in a lawsuit and was offered four different payment alternatives by the defendant's insurance company. The interest rate is $8\%.$ Ignoring the tax

considerations, which of the following four alternatives has the highest present value $($and thus is the best option$)?$ Support your answer with the appropriate calculations. $$180,000$ now. $$54,000$ per year for the next $4$ years $($end$-$of$-$year payments$)$ $$9,000$ now and then $$25,000$ per year for the next $10$ years $($end$-$of$-$year payments$).$ Hint:

Calculate the present value of the initial $$9,000$ separately. Then calculate the present value the $$25,000$ annuity separately. Finally, add the two present value amounts together to get the overall present value. $$13,100$ per year for the next $10$ years $($end$-$of$-$year payment$)$ plus a lump sum payment of$$200,000$ at the end of the ${11}^{th}$ year.

Hint: Calculate the present value of the $$13,10010-$year annuity separately. Then calculate the present value the $$200,000$ payment

received at the end of year $11$ separately. Finally, add the two present value amounts together to get the overall present value.