Question

Mr. Lee has won the lottery! He spent all the money to buy a Lamborghini sports car at a price of $3,900,000. Unfortunately, the value of the car depreciates quickly. Typically, a Lamborghini loses 3/5 of its value every two years. If Mr. Lee sells the car after five years of ownership, how much money will he receive?

Answer 1

After five years of depreciation, Mr. Lee would receive $436,800 for the Lamborghini. We calculated this by applying the two-year depreciation rate of 3/5 to the initial value, and then applied a one-year estimated depreciation for the fifth year.

Step-by-step explanation:

Calculating Car Depreciation and Expected Sale Price

Mr. Lee bought a Lamborghini for $3,900,000, and the car depreciates by 3/5 of its value every two years. To calculate the expected sale price after five years, we need to account for two full two-year periods and an additional year of depreciation.

After the first two years, the value of the car will be:

$3,900,000 × (1 - 3/5) = $3,900,000 × 2/5 = $1,560,000

After the next two years (four years in total), the continuing depreciation will leave the value at:

$1,560,000 × 2/5 = $624,000

Now, we must consider the depreciation in the fifth year. Since depreciation is provided on a two-year basis, we'll make a linear approximation for the one year. Assuming a straight-line depreciation, we divide the two-year depreciation rate by two to find the annual rate:

3/5 ÷ 2 = 3/10

Hence, for the fifth year, the car depreciates by another 3/10 of its fourth-year value:

$624,000 × (1 - 3/10) = $624,000 × 7/10 = $436,800

Therefore, after five years, Mr. Lee would receive $436,800 if he sells the Lamborghini.