a new car depreciated by 20% in its first year. each succeeding year it depreciated by 10% assume the car is still in good working condition after 10 years. if the car costs $25,000 calculate the value of the car after 10 years. express your answer to the nearest $10.
please help and show me your steps in working out this equation
After the first year the value is
25000(.8) = 20000
so after the next 9 years depreciating at 10% would leave
20000(.9)^9
7748.41 or 7750
To calculate the value of the car after 10 years, we can use the concept of compound interest/ depreciation. Here are the steps to calculate it:
1. Calculate the value of the car after the first year:
The car depreciated by 20%, so the value after the first year is:
$25,000 - (20% of $25,000) = $25,000 - $5,000 = $20,000
2. Calculate the value of the car after the second year:
The car depreciated by 10%, so the value after the second year is:
$20,000 - (10% of $20,000) = $20,000 - $2,000 = $18,000
3. Continue this process for each succeeding year until the tenth year:
The value after the third year: $18,000 - (10% of $18,000) = $16,200
The value after the fourth year: $16,200 - (10% of $16,200) = $14,580
The value after the fifth year: $14,580 - (10% of $14,580) = $13,122
The value after the sixth year: $13,122 - (10% of $13,122) = $11,810
The value after the seventh year: $11,810 - (10% of $11,810) = $10,629
The value after the eighth year: $10,629 - (10% of $10,629) = $9,566
The value after the ninth year: $9,566 - (10% of $9,566) = $8,609
The value after the tenth year: $8,609 - (10% of $8,609) = $7,748
Therefore, the value of the car after 10 years is approximately $7,750.