Thomas installed a new stove in his restaurant. At the time of installation, the stove had a value of $800....

1. TRANSLATE the problem information

• Given information:
  • Initial stove value: $800
  • Annual depreciation: 20% of previous year's value
  • Time period: 2 years
• What this tells us: Each year the stove keeps \(\mathrm{100\% - 20\% = 80\%}\) of its value from the previous year

2. INFER the calculation approach

• This is compound depreciation - each year's depreciation is based on that year's starting value, not the original $800
• We need to apply the 80% retention rate twice: once for each year
• Formula approach: Final Value = Initial Value × (retention rate)^(number of years)

3. SIMPLIFY the calculations

• Method 1 (year by year):
  • After year 1: \(\$800 \times 0.80 = \$640\)
  • After year 2: \(\$640 \times 0.80 = \$512\)
• Method 2 (compound formula):
  • After 2 years: \(\$800 \times (0.80)^2 = \$800 \times 0.64 = \$512\)

Answer: B. $512

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students miss that this is compound depreciation and instead calculate simple depreciation based on the original value each year.

They think: "20% of $800 is $160, so after 2 years it loses \(\$160 + \$160 = \$320\)"
This gives them \(\$800 - \$320 = \$480\)

This leads them to select Choice A ($480)

Second Most Common Error:

Poor TRANSLATE reasoning: Students correctly understand compound depreciation but stop after calculating just one year.

After correctly finding the first year value of $640, they select this as their final answer without continuing to the second year.

This causes them to select Choice D ($640)

The Bottom Line:

The key challenge is recognizing that "20% of the previous year's estimated value" means compound depreciation, where each calculation builds on the result of the previous year, not on the original value.