A car is purchased for $19000. After each year, the resale value decreases by 30% . What will the resale value be after 4 years?
Set up a book value function B(t) where t is the number of years after purchase date. If an asset decreases by 30%, we subtract it from the original 100% of the starting value at time t:
B(t) = 19,000(1-0.3)^t
Simplifying this, we get:
B(t) = 19,000(0.7)^t <-- If an asset decreases by 30%, it keeps 70% of it's value from the prior period
The problem asks for B(4):
B(4) = 19,000(0.7)^4
B(4) = 19,000(0.2401)
B(4) = 4,561.90
Set up a book value function B(t) where t is the number of years after purchase date. If an asset decreases by 30%, we subtract it from the original 100% of the starting value at time t:
B(t) = 19,000(1-0.3)^t
Simplifying this, we get:
B(t) = 19,000(0.7)^t <-- If an asset decreases by 30%, it keeps 70% of it's value from the prior period
The problem asks for B(4):
B(4) = 19,000(0.7)^4
B(4) = 19,000(0.2401)
B(4) = 4,561.90