The value of $500 after four years is $610
Step-by-step explanation:
It is given that, the value of $500 increases at a rate of 5% per year.
The exponential formula is given by [tex]y = ab^{x}[/tex].
where,
The growth factor b is replaced by either (1 + r) or by (1 - r).
where, r is the rate per year.
b= (1+r) represents the increase in growth rate.
b= (1-r) represents the decrease in growth rate.
Here, the growth rate is increased. So the formula is given by [tex]y = a(1+r)^{n}[/tex]
where,
To find y value :
⇒ [tex]y = 500(1+0.05)^{4}[/tex]
⇒ [tex]y = 500 (1.05)^{4}[/tex]
⇒ [tex]y = 500 \times 1.22[/tex]
⇒ [tex]y = 610[/tex]
Therefore, the value of the item after four years is $610.
