The value of a collector's item is expected to increase exponentially each year. The item is purchases for $500 and its value increases at a rate of 5% per year. Find the value of the item after 4 years.

The value of the item after 4 years is $608

Step-by-step explanation:

In this question, we are tasked with calculating the value of an item which increases at a particular percentage after 4 years.

To calculate the new value, we will be needing an exponential model to get it

mathematically this can be represented as;

V = I (1 + r) ^t

where V is the value after t years

I is the initial value which is $500 according to the question

r is the increase rate = 5% = 5/100 = 0.05

t is time which is 4 years

Plugging these values, we have

P = 500 (1+0.05) ^4

P = 500 (1.05) ^4

P = 607.75 which is approximately $608