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

Answer: $34728.75

Step-by-step 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.

Answer 2

Answer:

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