Question

Thirty years ago, Bruce Wayne bought a Batmobile for 729 million dollars. As the crime in Gotham City has been down for a while, he plans to sell it. How much can he get for the Batmobile today if the price goes down by 331/3% every 5 years?

Answer 1

The current price of the Batmobile can be calculated using compound depreciation over a period of 30 years, with a 33¼% value decrease every 5 years. Using the formula for compound depreciation, the initial price needs to be multiplied by (0.6667)^6 to find the final value.

Step-by-step explanation:

The question involves the calculation of the depreciating value of an asset over time using percentage decrease. The Batmobile's original price 30 years ago was 729 million dollars. According to the question, the price decreases by 33¼% every 5 years. First, we need to translate the percentage into a decimal to make the calculation easier. A decrease of 33¼% is equal to a decrease of 0.3333 (since 33¼% is the same as 33.33%). To find the depreciated value of the Batmobile after every 5 years, we multiply the current value by (1 - 0.3333). Therefore, after every 5 years, the Batmobile retains 1 - 0.3333 = 0.6667 (or 66.67%) of its value. Since 30 years have passed, we do this depreciation process a total of 30 ÷ 5 = 6 times.

We will use the formula for compound depreciation which is:
P_final = P_initial × (1 - depreciation_rate)^number_of_periods

Substituting the known values gives us:

P_final = 729,000,000 × (0.6667)^6

Calculating this value will give us the current price of the Batmobile.