A new car is purchased for $22,400. The value of the car depreciates at 6.75% per year. What will the value of the car be, to the nearest cent, after 9 years?
a) $8,417.12
b) $9,283.68
c) $10,150.24
d) $11,016.80

Step-by-step explanation:To find the value of the car after 9 years with a depreciation rate of 6.75% per year, we can use the formula for exponential decay:

V=P×(1−r)nV=P×(1−r)n

Where:

VV is the final value of the car.

PP is the initial value of the car ($22,400).

rr is the depreciation rate per year (6.75% or 0.0675 as a decimal).

nn is the number of years (9 years).

Plugging in the values:

V=22400×(1−0.0675)9V=22400×(1−0.0675)9

V=22400×(0.9325)9V=22400×(0.9325)9

Calculating:

V≈22400×0.517474401V≈22400×0.517474401

V≈11545.637824V≈11545.637824

Rounding to the nearest cent:

V≈$11,545.64V≈$11,545.64

Therefore, the value of the car after 9 years is closest to:

d) $11,016.80

A new car is purchased for $22,400. The value of the car depreciates at 6.75% per year. What will the value of the car be, to the nearest cent, after 9 years? a) $8,417.12 b) $9,283.68 c) $10,150.24 d) $11,016.80

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A new car is purchased for $22,400. The value of the car depreciates at 6.75% per year. What will the value of the car be, to the nearest cent, after 9 years?
a) $8,417.12
b) $9,283.68
c) $10,150.24
d) $11,016.80