Evan spent the summer earning money so he could buy the classics car of his dreams. He purchased the car for $2,295 from Fast Deal Freddie, the local used car salesman. Freddie told Evan that the car would increase by half its value after five years. Evan knows that this model appreciates 8% annually. Did Freddie try to trick Evan, or was his claim accurate?
according to Freddie ...
Value after 5 yrs
= 2295(1.08)^5 = 3372.11
What do you think?
actually all we have to do is look at
1.08^5
which is 1.469 or appr 147%
Freddie was pretty close
str
To determine if Freddie's claim was accurate, we need to calculate the future value of the car after five years and compare it to half of its original value.
Let's start by finding the future value of the car after five years, considering that it appreciates at a rate of 8% annually.
Future Value = Original Value * (1 + Annual Appreciation Rate)^Number of Years
Original Value = $2,295
Annual Appreciation Rate = 8%
Number of Years = 5
Future Value = $2,295 * (1 + 0.08)^5
Calculating the future value:
Future Value = $2,295 * (1.08)^5
Future Value = $2,295 * 1.4693
Future Value = $3,367.22
Now, let's compare the future value of the car to half of its original value:
Half of the Original Value = $2,295 / 2
Half of the Original Value = $1,147.50
Based on the calculations, the future value of the car after five years is $3,367.22, which is greater than half of its original value, $1,147.50.
Therefore, Freddie's claim that the car would increase by half its value after five years is accurate.
To determine whether Freddie's claim about the car appreciating in value was accurate, let's calculate the future value of the car after five years considering the annual appreciation rate of 8%.
First, let's calculate the appreciation for each year. Since the car appreciates at a rate of 8%, we can calculate the appreciation as follows:
Year 1: $2,295 * 8% = $183.60
Year 2: ($2,295 + $183.60) * 8% = $190.36
Year 3: ($2,295 + $183.60 + $190.36) * 8% = $197.62
Year 4: ($2,295 + $183.60 + $190.36 + $197.62) * 8% = $205.46
Year 5: ($2,295 + $183.60 + $190.36 + $197.62 + $205.46 ) * 8% = $213.92
Now, let's calculate the future value after five years by adding the total appreciation to the initial purchase price:
Future Value = $2,295 + $183.60 + $190.36 + $197.62 + $205.46 + $213.92 = $3,285.96
Therefore, the car's future value after five years is $3,285.96.
Now, let's check if Freddie's claim matches our calculation. According to Freddie, the car would increase by half its value after five years. Half of the initial purchase price is $2,295 / 2 = $1,147.50.
$1,147.50 is not equal to $3,285.96, which means Freddie's claim was inaccurate. He tried to trick Evan with an incorrect statement about the car's appreciation.
In conclusion, Freddie tried to trick Evan with a false claim about the car appreciating in value. The actual future value of the car after five years is $3,285.96.