$3.$ You decide to buy a new car. After choosing your vehicle, the dealership offers you $3$ payment

options, of which two are financing offers. The annual interest rate is $12\%.$ Which option do you choose,

based on the present value of these $3$ options? Show your work and explain your calculations.

Option $1$: Pay $$14,906,$ due today.

Option $2$: Pay $$1,000$ per month for $20$ months.

Option $3$: Pay $$500$ per month for $20$ months and $$10,000$ at the end of the $20$th month.