A new car is purchased for 19900 dollars. The value of the car depreciates at per year. What
will the value of the car be, to the nearest cent, after 8 years?

Question

A new car is purchased for 19900 dollars. The value of the car depreciates at $$ 7.5 \% $$ per year. What will the value of the car be, to the nearest cent, after 8 years?

UpStudy AI · Accepted Answer

To find the value of the car after 8 years, we can use the formula for depreciation:

$$ \text{Value after depreciation} = \text{Initial value} \times (1 - \text{Depreciation rate})^{\text{Number of years}} $$

Given:
- Initial value of the car = $19900
- Depreciation rate = 7.5% per year
- Number of years = 8

Substitute the values into the formula:

$$ \text{Value after depreciation} = 19900 \times (1 - 0.075)^8 $$

Now, we can calculate the value of the car after 8 years.
Calculate the value by following steps:
- step0: Calculate:
  $$19900\left(1-0.075\right)^{8}$$
- step1: Subtract the numbers:
  $$19900\times 0.925^{8}$$
- step2: Convert the expressions:
  $$19900\left(\frac{37}{40}\right)^{8}$$
- step3: Simplify:
  $$19900\times \frac{37^{8}}{40^{8}}$$
- step4: Rewrite the expression:
  $$20\times 995\times \frac{37^{8}}{40^{8}}$$
- step5: Rewrite the expression:
  $$20\times 995\times \frac{37^{8}}{20^{8}\times 2^{8}}$$
- step6: Reduce the numbers:
  $$995\times \frac{37^{8}}{20^{7}\times 2^{8}}$$
- step7: Rewrite the expression:
  $$5\times 199\times \frac{37^{8}}{20^{7}\times 2^{8}}$$
- step8: Rewrite the expression:
  $$5\times 199\times \frac{37^{8}}{5^{7}\times 4^{7}\times 2^{8}}$$
- step9: Reduce the numbers:
  $$199\times \frac{37^{8}}{5^{6}\times 4^{7}\times 2^{8}}$$
- step10: Multiply:
  $$\frac{199\times 37^{8}}{65536000000}$$
The value of the car after 8 years will be approximately $10665.64 to the nearest cent.
The car's value after 8 years is approximately $10,665.64.

A new car is purchased for 19900 dollars. The value of the car depreciates at per year. What
will the value of the car be, to the nearest cent, after 8 years?

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A new car is purchased for 19900 dollars. The value of the car depreciates at per year. What will the value of the car be, to the nearest cent, after 8 years?

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A new car is purchased for 19900 dollars. The value of the car depreciates at per year. What
will the value of the car be, to the nearest cent, after 8 years?