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The 2006 price of a certain type of car is $26,300. Estimate the price of the same car in the year 2013. Assume a constant annual inflation rate of 2.1%. Give a number of significant figures consistent with the 2006 price given

User Jumel
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Final answer:

To estimate the price of the car in 2013, we use the compound interest formula with an initial price of $26,300, an annual inflation rate of 2.1%, over 7 years, resulting in an estimated price of approximately $30,400.

Step-by-step explanation:

The question asks to estimate the price of a type of car in 2013 given its price in 2006 with an annual inflation rate. To calculate this, we can use the formula for compound interest which is P(1 + r)^n, where P is the principal amount (initial price), r is the rate of interest (inflation rate), and n is the number of years. In this case, P is $26,300, r is 2.1% or 0.021, and n is 7 (from 2006 to 2013).

Using the formula:

  • Price in 2013 = $26,300 * (1 + 0.021)^7
  • Price in 2013 = $26,300 * (1.021^7)
  • Price in 2013 ≈ $26,300 * 1.155 (rounded to three decimal places)
  • Price in 2013 ≈ $30,369.50

This result should be reported with a number of significant figures consistent with the original price, which is $26,300. Therefore, the estimated price of the car in 2013, consistent with the given significant figures, is approximately $30,400.

User George Poliovei
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