Lillian buts a car for $27,869. The next year, Lillian finds out that it is worth $25,197. The next year, it is only $24,525. If this trend continues, how much will Lillian’s far be worth in 9 years?

Answer 1

To determine how much Lillian's car will be worth in 9 years, we first need to identify the trend in the car's depreciation.

1. Calculate the depreciation amount from year 1 to year 2:

   • Year 1 value: $27,869
   • Year 2 value: $25,197
   • Depreciation = $27,869 - $25,197 = $2,672

2. Calculate the depreciation amount from year 2 to year 3:

   • Year 2 value: $25,197
   • Year 3 value: $24,525
   • Depreciation = $25,197 - $24,525 = $672

3. Determine the trend in depreciation:

   • The depreciation decreased from $2,672 to $672. We can calculate the rate of depreciation from Year 1 to Year 2 and Year 2 to Year 3.
   • First year depreciation rate: \( \frac{2672}{27869} \approx 0.096 \) or 9.6%
   • Second year depreciation rate: \( \frac{672}{25197} \approx 0.027 \) or 2.7%

From this data, it appears that the car's depreciation is slowing down over the years. For simplicity, let's assume that after the first two years, the depreciation amount becomes constant, as a rough estimate of the car's future value.

We can take the average of the depreciation seen so far.

1. Average depreciation over the two years: \[ \text{Average depreciation} = \frac{2672 + 672}{2} = \frac{3344}{2} = 1672 \]

2. Calculate the depreciation for the next 9 years:

   • Since we have already observed 3 years, we have 6 more years to account for.
   • Total depreciation over the next 6 years: \[ 6 \times 672 = 4032 \]

3. Subtract this depreciation from the current value (Year 3 value of $24,525): \[ \text{Value in 9 years} = 24525 - 4032 = 20493 \]

Thus, if the trend continues, Lillian's car will be worth approximately $20,493 in 9 years.