Car Depreciation worksheet

1. Average yearly depreciation: 6.51%

1. The share of the price the car keeps is the current value divided by the price

   $\frac{\mathrm{\$25,000.00}}{\mathrm{\$35,000.00}}$$=0.714286$

2. Spread that evenly over 5 years by raising it to the power 1/5

   ${\left(0.714286\right)}^{\frac{1}{5}}$$=0.93492$

3. The yearly rate is the share lost each year: 1 minus that, as a percent

   $\left(1-0.93492\right)\times 100$$=\mathrm{6.508\%}$

4. Total value lost is the price minus the current value

   $\mathrm{\$35,000.00}-\mathrm{\$25,000.00}$$=\mathrm{\$10,000.00}$

2. Estimated value after 5 years: $13,623.51

1. After the first year the car keeps 82% of its price

   $\mathrm{\$29,000.00}\times \left(1-0.18\right)$$=\mathrm{\$23,780.00}$

2. Each of the next 4 years it keeps 87% of the previous value

   $\mathrm{\$23,780.00}\times {\left(1-0.13\right)}^4$$=\mathrm{\$13,623.51}$

3. Depreciation is the purchase price minus the value now

   $\mathrm{\$29,000.00}-\mathrm{\$13,623.51}$$=\mathrm{\$15,376.49}$

4. Divide by the price to see the loss as a share of what you paid

   $\frac{\mathrm{\$15,376.49}}{\mathrm{\$29,000.00}}$$=\mathrm{53.0224\%}$

3. Average yearly depreciation: 10.91%

1. The share of the price the car keeps is the current value divided by the price

   $\frac{\mathrm{\$17,500.00}}{\mathrm{\$35,000.00}}$$=0.5$

2. Spread that evenly over 6 years by raising it to the power 1/6

   ${\left(0.5\right)}^{\frac{1}{6}}$$=0.890899$

3. The yearly rate is the share lost each year: 1 minus that, as a percent

   $\left(1-0.890899\right)\times 100$$=\mathrm{10.9101\%}$

4. Total value lost is the price minus the current value

   $\mathrm{\$35,000.00}-\mathrm{\$17,500.00}$$=\mathrm{\$17,500.00}$

4. Average yearly depreciation: 7.48%

1. The share of the price the car keeps is the current value divided by the price

   $\frac{\mathrm{\$20,000.00}}{\mathrm{\$29,500.00}}$$=0.677966$

2. Spread that evenly over 5 years by raising it to the power 1/5

   ${\left(0.677966\right)}^{\frac{1}{5}}$$=0.925213$

3. The yearly rate is the share lost each year: 1 minus that, as a percent

   $\left(1-0.925213\right)\times 100$$=\mathrm{7.4787\%}$

4. Total value lost is the price minus the current value

   $\mathrm{\$29,500.00}-\mathrm{\$20,000.00}$$=\mathrm{\$9,500.00}$

5. Average yearly depreciation: 18.1%

1. The share of the price the car keeps is the current value divided by the price

   $\frac{\mathrm{\$22,500.00}}{\mathrm{\$50,000.00}}$$=0.45$

2. Spread that evenly over 4 years by raising it to the power 1/4

   ${\left(0.45\right)}^{\frac{1}{4}}$$=0.819036$

3. The yearly rate is the share lost each year: 1 minus that, as a percent

   $\left(1-0.819036\right)\times 100$$=\mathrm{18.0964\%}$

4. Total value lost is the price minus the current value

   $\mathrm{\$50,000.00}-\mathrm{\$22,500.00}$$=\mathrm{\$27,500.00}$

6. Average yearly depreciation: 12.94%

1. The share of the price the car keeps is the current value divided by the price

   $\frac{\mathrm{\$20,000.00}}{\mathrm{\$40,000.00}}$$=0.5$

2. Spread that evenly over 5 years by raising it to the power 1/5

   ${\left(0.5\right)}^{\frac{1}{5}}$$=0.870551$

3. The yearly rate is the share lost each year: 1 minus that, as a percent

   $\left(1-0.870551\right)\times 100$$=\mathrm{12.9449\%}$

4. Total value lost is the price minus the current value

   $\mathrm{\$40,000.00}-\mathrm{\$20,000.00}$$=\mathrm{\$20,000.00}$

7. Estimated value after 5 years: $9,728.96

1. After the first year the car keeps 82% of its price

   $\mathrm{\$25,000.00}\times \left(1-0.18\right)$$=\mathrm{\$20,500.00}$

2. Each of the next 4 years it keeps 83% of the previous value

   $\mathrm{\$20,500.00}\times {\left(1-0.17\right)}^4$$=\mathrm{\$9,728.96}$

3. Depreciation is the purchase price minus the value now

   $\mathrm{\$25,000.00}-\mathrm{\$9,728.96}$$=\mathrm{\$15,271.04}$

4. Divide by the price to see the loss as a share of what you paid

   $\frac{\mathrm{\$15,271.04}}{\mathrm{\$25,000.00}}$$=\mathrm{61.0842\%}$

8. Estimated value after 5 years: $20,430.75

1. After the first year the car keeps 83% of its price

   $\mathrm{\$45,000.00}\times \left(1-0.17\right)$$=\mathrm{\$37,350.00}$

2. Each of the next 4 years it keeps 86% of the previous value

   $\mathrm{\$37,350.00}\times {\left(1-0.14\right)}^4$$=\mathrm{\$20,430.75}$

3. Depreciation is the purchase price minus the value now

   $\mathrm{\$45,000.00}-\mathrm{\$20,430.75}$$=\mathrm{\$24,569.25}$

4. Divide by the price to see the loss as a share of what you paid

   $\frac{\mathrm{\$24,569.25}}{\mathrm{\$45,000.00}}$$=\mathrm{54.5983\%}$

9. Estimated value after 4 years: $27,337.50

1. After the first year the car keeps 75% of its price

   $\mathrm{\$50,000.00}\times \left(1-0.25\right)$$=\mathrm{\$37,500.00}$

2. Each of the next 3 years it keeps 90% of the previous value

   $\mathrm{\$37,500.00}\times {\left(1-0.1\right)}^3$$=\mathrm{\$27,337.50}$

3. Depreciation is the purchase price minus the value now

   $\mathrm{\$50,000.00}-\mathrm{\$27,337.50}$$=\mathrm{\$22,662.50}$

4. Divide by the price to see the loss as a share of what you paid

   $\frac{\mathrm{\$22,662.50}}{\mathrm{\$50,000.00}}$$=\mathrm{45.325\%}$

10. Estimated value after 6 years: $13,078.56

1. After the first year the car keeps 82% of its price

   $\mathrm{\$32,000.00}\times \left(1-0.18\right)$$=\mathrm{\$26,240.00}$

2. Each of the next 5 years it keeps 87% of the previous value

   $\mathrm{\$26,240.00}\times {\left(1-0.13\right)}^5$$=\mathrm{\$13,078.56}$

3. Depreciation is the purchase price minus the value now

   $\mathrm{\$32,000.00}-\mathrm{\$13,078.56}$$=\mathrm{\$18,921.44}$

4. Divide by the price to see the loss as a share of what you paid

   $\frac{\mathrm{\$18,921.44}}{\mathrm{\$32,000.00}}$$=\mathrm{59.1295\%}$