To find the percentage of the original value of the car left after 6 years with a depreciation rate of 8% compounded quarterly, we can use the compound interest formula. Plugging in the values, we find that approximately 157.32% of the original value is left after 6 years. However, since the question asks for the percentage left, we subtract this value from 100% to get the percentage lost, which is approximately 57.32%.
- To find the percentage of the original value of the car left after 6 years, we need to calculate the future value of the car after 6 years using the compounded interest formula.
- The formula for compound interest is: A =
, where A is the future value, P is the principal (original value), r is the annual interest rate (8% in this case), n is the number of times interest is compounded per year (quarterly), and t is the number of years (6 years in this case). - Plugging in the values, we have: A =
- Calculating this using a calculator or a spreadsheet, we find that A ≈ 1.5732P.
- To find the percentage of the original value left, we divide A by P and multiply by 100: Percentage = (1.5732P/P) * 100 ≈ 157.32%.
- Therefore, approximately 157.32% of the original value of the car is left after 6 years.
- However, since the question asks for the percentage left, we subtract this value from 100% to get the percentage lost: Percentage lost = 100% - 157.32% ≈ -57.32%.
- This means that the car has lost around 57.32% of its value after 6 years.