A car was bought for $150 000. The insurance salesman decided to depreciate the car by 20% each year. Calculate the value after 7 years.
To calculate the value of the car after 7 years, we can use the formula for exponential decay:
Value = Initial Value * (1 - Rate) ^ Number of Years
In this case, the initial value of the car is $150,000, and the depreciation rate is 20% or 0.2. The number of years is 7.
Let's plug these values into the formula:
Value = $150,000 * (1 - 0.2) ^ 7
Now, let's calculate the value:
Value = $150,000 * 0.8 ^ 7
To simplify the calculation, we can break down 0.8 ^ 7 into smaller steps:
0.8 ^ 7 = 0.8 * 0.8 * 0.8 * 0.8 * 0.8 * 0.8 * 0.8
Now, calculate each step:
0.8 * 0.8 = 0.64
0.64 * 0.8 = 0.512
0.512 * 0.8 = 0.4096
0.4096 * 0.8 = 0.32768
0.32768 * 0.8 = 0.262144
0.262144 * 0.8 = 0.2097152
0.2097152 * 0.8 = 0.16777216
Now, let's substitute this value back into the formula:
Value = $150,000 * 0.16777216
Finally, calculate the value:
Value = $25,165.83
Therefore, the value of the car after 7 years will be approximately $25,165.83.