Question

the value of a collectors item is expected to increase exponentially each year. the item is purchased for $500 and its value increases at a rate of 5% per year. find the value of the item after 4 years. $607.75 $578.81 $1,687.50 $2,531.25

Explanation:

Step1: Recall exponential growth formula

The exponential growth formula is $A = P(1 + r)^t$, where $P$ is initial value, $r$ is annual rate, $t$ is time in years.

Step2: Identify given values

$P = 500$, $r = 0.05$, $t = 4$

Step3: Substitute values into formula

$A = 500(1 + 0.05)^4 = 500(1.05)^4$

Step4: Calculate $(1.05)^4$

$(1.05)^4 = 1.05\times1.05\times1.05\times1.05 = 1.21550625$

Step5: Compute final value

$A = 500\times1.21550625 = 607.753125$

Answer:

$607.75$