Question

logan has a collection of vintage action figures that is worth $400. if the collection appreciates at a rate 4% per year, which equation represents the value of the collection after 6 years? answer \\( \bigcirc \\ v = 400(1 + 0.04)(1 + 0.04)(1 + 0.04)(1 + 0.04) \\) \\( \bigcirc \\ v = 400(0.04)^6 \\) \\( \bigcirc \\ v = 400(0.96)^6 \\) \\( \bigcirc \\ v = 400(1.04)^6 \\)

Explanation:

Step1: Recall compound appreciation formula

The formula for compound appreciation is $V = P(1 + r)^t$, where $P$ is initial value, $r$ is annual rate, $t$ is time in years.

Step2: Identify given values

$P = 400$, $r = 0.04$, $t = 6$

Step3: Plug values into formula

Substitute the values into the formula: $V = 400(1 + 0.04)^6 = 400(1.04)^6$

Step4: Eliminate incorrect options

• First option only compounds for 4 years, not 6.
• Second option uses only the rate, no growth factor.
• Third option uses a depreciation factor ($0.96 = 1 - 0.04$), which is for loss in value.

Answer:

$V = 400(1.04)^6$