Question

You begin your first day as a police officer earning $30,000/yr. Assuming that you obtain a full 5% increase each year, what will your salary be in three years?​

Answer 1

The equation for the amount of salary after x number of years is given by:

`y = a(1+r)^x`

where

a is the initial amount

x represents the number of years and

r represents the growth rate( in decimal)

As per the statement:

You begin your first day as a police officer earning $30,000/yr

⇒ a= 30,000

It is also given that you obtain a full 5% increase each year,

⇒
`r = 5\% = 0.05`

then;

`y = 30,000(1+0.05)^x`

`y = 30,000(1.05)^x` ....[1]

we have to find the salary in three years.

⇒
`x = 3`

Substitute this value in [1] we have

`y = 30,000(1.05)^3`

Simplify:

`y = \$ 34,4728.75`

therefore, your salary be in three years will be $34,4728.75

Answer 2

Answer: $34728.75

Explanation:

Given: The salary of a police officer for a year P= $30,000

The rate of increase r= 5% = 0.05 per year

We know that the compound amount after t years at rate of intersect r is given by :-

`A=P(1+r)^t`

Then, the compound amount after 3 years is given by :-

`A=30,000(1+0.05)^3\\\Rightarrow\ A=30,000(1.05)^3\\\Rightarrow\ A=34728.75`

Hence, the salary of policeman after 3 years will be $34728.75.