A car decreases in value by 20% for the first year, and for each later year by 12% of its value at the beginning of that year. Calculate the percentage decrease in the value of the car after 3 years. Answer not 44% if that is what you got.
initial value = Vi
after one year v = .8 Vi
after two years v = .8 Vi *.88
after three years
v = .8 Vi *.88 * .88 = .61952 Vi
1 -.61952 = .38048
so
38.048 percent
To calculate the percentage decrease in the value of the car after 3 years, we need to calculate the value of the car at the end of each year.
Let's assume the initial value of the car is 100. After the first year, the car's value will decrease by 20% of its initial value, leaving it at 80. After the second year, the value of the car will decrease by 12% of its value at the beginning of that year. The value at the beginning of the second year is 80, so the car's value at the end of the second year will be 80 - (12% of 80) = 80 - 9.6 = 70.4.
Similarly, after the third year, the car's value will decrease by 12% of its value at the beginning of the third year. The value at the beginning of the third year is 70.4, so the car's value at the end of the third year will be 70.4 - (12% of 70.4) = 70.4 - 8.45 = 61.95.
Now, to calculate the percentage decrease, we need to find the difference between the initial value and the final value of the car, and then divide it by the initial value.
Percentage decrease = (Initial value - Final value) / Initial value * 100
Percentage decrease = (100 - 61.95) / 100 * 100
Percentage decrease = 38.05 / 100 * 100
Percentage decrease = 38.05%
Therefore, the percentage decrease in the value of the car after 3 years is 38.05%.