Question

nabhitha has a collection of vintage action figures that is worth $420. if the collection appreciates at a rate of 13% per year, which equation represents the value of the collection after 6 years?
answer
\\( v = 420(1 + 0.13)(1 + 0.13)(1 + 0.13) \\)
\\( v = 420(0.87)^6 \\)
\\( v = 420(1.13)^6 \\)
\\( v = 420(0.13)^6 \\)

Explanation:

Step1: Recall 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

$P = 420$, $r = 0.13$, $t = 6$

Step3: Plug values into formula

Substitute the values into the formula: $V = 420(1 + 0.13)^6 = 420(1.13)^6$

Step4: Eliminate incorrect options

• Option1 only compounds 3 times, not 6.
• Option2 uses depreciation factor $(0.87=1-0.13)$, wrong for appreciation.
• Option4 only multiplies by the rate, not the growth factor.

Answer:

$V = 420(1.13)^6$