Question

Your starting salary at a new company is $45,300 and it increase by 3.25% each year. How many

years will it take for your salary to reach $75,000?
"Careful with rounding too soon
Solve

Answer 1

it take 16 years for your salary to reach $75,000 .

Explanation:

Here we have , Your starting salary at a new company is $45,300 and it increase by 3.25% each year. How many years will it take for your salary to reach $75,000. Let's find out:

Let t be the number of years after which $45,300 is increased to $75,000 at increase of 3.25% . So , equation from the above statement is given as :

⇒
`75000 = 45300( 1 + (3.25)/(100) )^t`

⇒
`75000 = 45300( 1 +0.0325 )^t`

⇒
`75000 = 45300( 1.0325 )^t`

⇒
`(75000)/(45300) = ( 1.0325 )^t`

⇒
`( 1.0325 )^t = 1.65562914`

Taking anti log with base 1.0325:

⇒
`t = Log_1._0_3_2_5(1.65562914)`

⇒
`t = 15.76`

On rounding off we get :

⇒
`t = 16`

Therefore , it take 16 years for your salary to reach $75,000 .