For The given problem, The initial value of the car is 23700 dollars.
After one year, the price of the car depreciates by 13.5% per year. So , the new price of car after one year becomes:
P1=23700−23700⋅(13.5/100)=23700⋅(1−13.5/100)dollars
Again, taking P1 as base price, the price of the car now depreciates by 13.5% per year. So , the new price (in dollars) of car after second year becomes:
P2=P1−P1⋅(13.5/100)=P1⋅(1−13.5/100)=23700⋅(1−13.5/100)⋅(1−13.5/100)=23700⋅(1−13.5/100)2dollars
Following the same, the new price of car after third year becomes:
P3=P2−P2⋅(13.5/100)=P2⋅(1−13.5/100)=23700⋅(1−13.5/100)2⋅(1−13.5/100)=23700⋅(1−13.5/100)3dollars
And, so on as we continue to move to tenth year, the new price of car at the end of tenth year becomes:
P10=23700⋅(1−13.5/100)10=23700⋅(1−0.135)10=23700⋅0.86510=(23700⋅0.2345098)dollars=(23700⋅0.2345098⋅100)cents=555788cents
So the value of the car to the nearest cent after 10 years becomes 555788 cents.
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