the value of a collectors item is expected to increase exponentially each year. the item is purchased for…

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. $578.81 $607.75 $1687.50 $2531.25

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. $578.81 $607.75 $1687.50 $2531.25

Answer

Explanation:

Step1: Identify the formula

The formula for exponential - growth is $A = P(1 + r)^t$, where $P$ is the initial amount, $r$ is the rate of growth as a decimal, and $t$ is the number of years.

Step2: Convert the rate to a decimal

Given $r = 5%=0.05$, $P = 500$, and $t = 4$.

Step3: Substitute the values into the formula

$A=500\times(1 + 0.05)^4$. First, calculate $(1 + 0.05)^4=(1.05)^4=1.05\times1.05\times1.05\times1.05 = 1.21550625$. Then, $A = 500\times1.21550625=607.753125\approx607.75$.

Answer:

$607.75$ (corresponding to the option $$607.75$)