Amy Lloyd is interested in leasing a new Honda and has contacted three automobile dealers for pricing information. Each dealer offered Amy a closed-end 36-month lease with no down payment due at the time of signing. Each lease includes a monthly charge and a mileage allowance. Additional miles receive a surcharge on a per-mile basis. The monthly lease cost, the mileage allowance, and the cost for additional miles follow:

Dealer Monthly Cost Mileage Allowance Cost per Additional Mile
Hepburn Honda $299 36,000 $0.15
Midtown Motors $310 45,000 $0.20
Hopkins Automotive $325 54,000 $0.15

Amy decided to choose the lease option that will minimize her total 36-month cost. The difficulty is that Amy is not sure how many miles she will drive over the next three years. For purposes of this decision, she believes it is reasonable to assume that she will drive 12,000 miles per year, 15,000 miles per year, or 18,000 miles per year. With this assumption Amy estimated her total costs for the three lease options.

Construct a payoff table for Amy's problem.

For 12000, 15000 and 18000 miles per year respectively.

Dealer = Hepburn Honda:

10764 USD, 12,114 USD, 13464 USD

Dealer = Midtown Motors:

11,160  USD, 11,160 USD, 12,960 USD

Dealer = Hopkins Automotive:

11,700 USD, 11,700 USD, 11,700 USD

Explanation:

Payoff Table Construction:

The assumption of miles per year will definitely help to calculate the overall cost. Here we go:

1. Assumption no: 1:

12000 miles = 1 year

24000 miles = 2 years

36000 miles = 3 years

Let's calculate the cost for Hepburn Honda Dealer:

Dealer = Hepburn Honda:

3 years = 36 months

For 12000 miles per year drive

For 3 years = 36000 miles

So, we have:

36(299) + 0.15(36000 - 36000) = 10764 USD

For 15000 miles per year drive

For 3 years = 45000 miles

36(299) + 0.15(45000-36000) =  12,114 USD

For 18000 miles per year drive

For 3 years = 54000 miles

36(299) + 0.15(54000-36000) = 13464 USD

Above are the calculations for dealer Hepburn Honda. Now, let's calculate for the second one.

Dealer = Midtown Motors:

For 12000 miles per year drive

For 3 years = 36000 miles

So, we have:

36(310) + 0.20 x max(36000 - 45000) = 11,160  USD

For 15000 miles per year drive

For 3 years = 45000 miles

36(310) + 0.15 x max(45000-45000) =  11,160 USD

For 18000 miles per year drive

For 3 years = 54000 miles

36(310) + 0.20 x max(54000-36000) = 12,960 USD

Above are the calculations for dealer Midtown Motors. Now, let's calculate for the third one.

Dealer = Hopkins Automotive:

For 12000 miles per year drive

For 3 years = 36000 miles

So, we have:

36(325) + 0.15 x max(36000 - 54000) = 11,700  USD

For 15000 miles per year drive

For 3 years = 45000 miles

36(325) + 0.15 x max(45000-54000) =  11,700 USD

For 18000 miles per year drive

For 3 years = 54000 miles

36(325) + 0.15 x max(54000-54000) = 11,700 USD

Payoff Table:

For 12000, 15000 and 18000 miles per year respectively.

Dealer = Hepburn Honda:

10764 USD, 12,114 USD, 13464 USD

Dealer = Midtown Motors:

11,160  USD, 11,160 USD, 12,960 USD

Dealer = Hopkins Automotive:

11,700 USD, 11,700 USD, 11,700 USD

23% is close to 25%, or the equivalent fraction 1/4.

The cost before tax and gratuity can be rounded to the tens place to $240.

1/4 of $240 is $60, which is close to Ami’s calculation.

Ami’s calculation is reasonable.

Anwser From Edgeinty

you have to put the parentheses like this:

in fact, you have to perform the operation inside parentheses first, and then proceed in order:

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