7.3 Depreciation and Appreciation

Depreciation and appreciation refer to the decrease or increase in the value of an asset over time.

Key Concepts:

• Depreciation:

  The reduction in the value of an asset over time, often due to wear and tear or obsolescence. \[ A = P(1 - r)^t \] where:
  • \(A\) = Value of the asset after time \(t\)
  • \(P\) = Initial value (purchase price)
  • \(r\) = Rate of depreciation (as a decimal)
  • \(t\) = Time in years

• Appreciation:

  The increase in the value of an asset over time, often due to demand or inflation. \[ A = P(1 + r)^t \] where:
  • \(A\) = Value of the asset after time \(t\)
  • \(P\) = Initial value
  • \(r\) = Rate of appreciation (as a decimal)
  • \(t\) = Time in years

Examples:

Example 1: Depreciation Calculation

A car was bought for \$15,000 and depreciates at a rate of 10\% per year. Find its value after 5 years.

Solution:

Step 1: Use the depreciation formula. \[ A = 15000 (1 - 0.10)^5 \] \[ A = 15000 (0.9)^5 \] \[ A = 15000 \times 0.59049 \] \[ A = 8857.35 \] Thus, the car's value after 5 years is **\$8857.35**.

Example 2: Appreciation Calculation

A house was purchased for \$120,000 and appreciates at a rate of 5\% per year. Find its value after 8 years.

Solution:

Step 1: Use the appreciation formula. \[ A = 120000 (1 + 0.05)^8 \] \[ A = 120000 (1.477455) \] \[ A = 177294.60 \] Thus, the house's value after 8 years is **\$177,294.60**.