How Did Motel 6 Go From $6 To $66?

 
When Motel 6 opened for business in 1962 they only charged $6 per night, hence their name.  They could not afford to keep that price forever, and since then their prices have continued to grow.
 

• What percent has their price increased since it first opened? (percent increase)
• What percent has the price increased annually on average? (compound interest)
• How has Motel 6 increased their prices compared to inflation?

 

These questions may be useful in helping students down the problem solving path:

• What is a guess that is too low for the percent increase?
• What is a guess that is too high for the percent increase?
• What is your best guess for the percent increase?
• What information do we need to know?

 

There are three challenges for this problem depending on the whether this is approached as a simple percent increase problem or a compound interest problem.  The first challenge is posed as a percent increase problem and the price has increased 1100% from $6 to $66 (or 1099.8% from $6 to $65.99).

The second and third challenges look at the problem from a historical perspective.  Using the generic compound interest formula and assuming:

• we are going from 1962 to 2013 for a total of 51 years
• interest is only compounded once a year

we get:

65.99 = 6(1 + r)^51

which ultimately gives us an average annual price increase percentage of approximately 4.81%.

The final challenge is an extension and involves comparing Motel 6’s average annual price increase percentage to the United States average annual inflation rate over the same period.  According to a US Inflation Calculator, if Motel 6 had only adjusted its prices to keep up with inflation, the price should be $45.61.  So, students will have to determine what interest rate would have resulted in that price.  That gives us:

45.61 = 6(1 + r)^51

which ultimately gives us an average annual inflation percentage of approximately 4.05%.

It is worth encouraging students to reflect on how an interest rate difference of only 0.76% has resulted in significantly different prices when compounded annually over 51 years.
 

• Current price at a Motel 6

• Original price at a Motel 6 in 1962

• Average annual inflation in the United States from 1962 to 2013

 

• CCSS 7.RP.3 Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.
• CCSS A-SSE.1b Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)ⁿ as the product of P and a factor not depending on P.
• CCSS F-BF.1 Write a function that describes a relationship between two quantities.
• CCSS F-IF.8b Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, y = (1.2)t/10, and classify them as representing exponential growth or decay.
• CCSS F-LE.1 Distinguish between situations that can be modeled with linear functions and with exponential functions.

 

• Motel 6 Corporate Profile
• US Inflation Calculator