Question

If an item is purchased at $500 and it’s value increases at a rate of 5% per year what is the value after four years

Answer 1

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 $y = ab^{x}$.

where,

• a is the initial  amount.
• b is the growth factor .

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 $y = a(1+r)^{n}$

where,

• The initial amount, a = 500.
• Rate, r = 5% = 5/100 = 0.05
• Number of years, n= 4.
• y = value of the item after 4 years

To find y value :

⇒ $y = 500(1+0.05)^{4}$

⇒ $y = 500 (1.05)^{4}$

⇒ $y = 500 \times 1.22$

⇒ $y = 610$

 Therefore, the value of the item after four years is $610.