Question

A new car is purchased for 16600 dollars. The value of the car depreciates at 9.75% per year. What will the value of the car be, to the nearest cent, after 8 years?

Answer 1

Answer:

After 8 years, the car will value $6593.

Step-by-step explanation:

1. Depreciation in year 1:

$16.600*0.0975=1618.5$

Value of the car at the end of year 1:

$16600-1618.5=14981.5$

2. Depreciation in year 2:

$14981.5*0.0975=1460.7$

Value of the car at the end of year 1:

$14981.5-1460.7=13520.3$

3. Depreciation in year 3:

$13520.3*0.0975=1318.2$

Value of the car at the end of year 1:

$13520.3-1318.2=12202.1$

4. Depreciation in year 4:

$12202.1*0.0975=1189.7$

Value of the car at the end of year 1:

$12202.1-1189.7=11012.4$

5. Depreciation in year 5:

$11012.4*0.0975=1073.7$

Value of the car at the end of year 1:

$11012.4-1073.7=9938.7$

5. Depreciation in year 5:

$9938.7*0.0975=969$

Value of the car at the end of year 1:

$9938.7-969=8969.7$

6. Depreciation in year 6:

$8969*0.0975=874.5$

Value of the car at the end of year 1:

$8969-874.5=8094.5$

7. Depreciation in year 7:

$8094.5*0.0975=789.2$

Value of the car at the end of year 1:

$8094.5-789.2=7305.3$

8. Depreciation in year 8:

$7305.3*0.0975=712.3$

Value of the car at the end of year 1:

$7305.3-712.3=6593$

Answer 2

A=16600(1-0.0975)^8
A==7,306.10