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.

$1)$ $$180,000$ now.

a$.$ PV$=180,000$ x $1=180,000$

$2)$ $$54,000$ per year for the next $4$ years $($end$-$of$-$year payments$)$

a$.$

$3)$ $$9,000$ now and then $$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.

$4)$ $$13,100$ per year for the next $10$ years $($end$-$of$-$year payments$)$ plus a lump sum payment of $$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.