Question

Sam has purchased a $30,000 car for his business. The car depreciates 30% every year. The car's value goes down by that percent every year. What will be the value of the car after the 5th year? Note: The car is 0 years old the first year is the secondary entry in the sequence. P.S Common ratio is 0.70.

Answer 1

The car's value after 5 years, considering a 30% annual depreciation rate with a common ratio of 0.70, will be approximately $5,042.10.

Step-by-step explanation:

The value of a car that depreciates by 30% per year can be calculated using the formula for geometric sequences, since depreciation in this case is a common ratio problem. In this scenario, the common ratio is 0.70 because each year the car retains 70% of its value from the previous year (100% - 30% depreciation = 70%). After 5 years, the car's value will be:

Value after 5 years = $30,000 × (0.70)^5

Now we calculate the value after 5 years step by step:

1. Calculate the common ratio to the power of the number of periods (years): (0.70)^5
2. Multiply the original value by the result from step 1.

Let's perform the calculations:

(0.70)^5 = 0.16807

Value after 5 years = $30,000 × 0.16807 = $5,042.10

So, after the fifth year, the car will approximately be worth $5,042.10.