You wish to buy a new car. The cost is $$20,000,$ and the interest rate is $10\%.$ The dealer gives you $4$ different offers:

Pay it all off today

Pay $$2000$ now and $$20,000$ next year

Don$$t pay a dime this year, but you will need to pay $$5000$ next year and $$20,000$ one year after that.

Pay according to this schedule: Today: $1000,$ Yr $1$: $2000$ Yr $2$: $3000,$ Yrs $3$: $3000$ Yr $4$: $15000$

Pay according to this schedule: Today: $0,$ Yr $1$: $0$ Yr $2$: $0$ Yrs $3$: $5000$ Yr $4$: $10000$ Yr $5$: $13,500$

table$[[$Cost$,20000,$Year,Offer$1,$Offer$2,$Offer$3,$Offer$4,$Offer$5],[$Rate$,10\%,0\%,20000,2000,0,1000,0],[,,1,,20000,5000,2000,0],[,2,,,20000,3000,5000,],[,,3,,$

$,,4000,10000],[,,4,,,,15000,13500]]$

Which deal should you take? Show a quantitative solution to the problem