First, lets talk through the logic here...
The car has an initial value of P. Each year it depreciates by 15%, which means it is now worth 85% of the original value, P (Since 100%-15% = 85%). This continues to happen each year. To find the value of the car in 7 years, we need to take into account 7 years of depreciation.
Value Year 2 = .85 (Value Year 1)
Value Year 3 = .85 (Value Year 2) = .85 (.85 (Value Year 1))
Value Year 4 = .85 (Value Year 3) = .85 (.85 ( .85 (Value Year 1))
Continue this same pattern until you have :
Value Year 7 = .85 (.85 (.85 (.85 (.85 (.85 (.85 (Value Year 1))))))) = .85^7 (Value Year 1)
We can make this final simplification since multiplication is commutative.
From the problem, Value Year 1 = $15,640. Therefore,
Value Year 7 = .85^7 (15640) ~ $5014
