You are purchasing a new car. The price you negotiated with a car dealer is $17,944, excluding sales tax. The local tax rate is 8.25%. What growth factor is associated with the sales tax rate?

Answer 1

17,944(1.0825)= $19,424.38 after tax price

It grew in price by 8.25%. It's growth rate = 8.25%

but growth rates often mean per some time period, such as annual interest, per year.

so? 8.25% was instantaneous and a $1480.38 increase per a micro infinitesimal second is an infinite growth rate. Odds are that's not the answer you want

Not clear what you're looking for though

maybe A= Pe^rt ?

with A/P = (1.0825)= e^.0825t

continuous growth rate

where A = after tax price,

P = before tax price

r=8.25% and t = years

1.0825 = e^.0825t

take natural logs of both sides

ln1.0825 = .0825t

t = ln1.0825/.0825

t = .07927318/.0825

t =about 0.96 years

call it about 11 1/2 months

8 1/4 % per .96 year growth rate

compounded continuously

= a little more than 8 1/4 per year

0.825/.96 = equivalent to about 8.59% annual growth rate

or maybe

A =P(1+r)^t

A/P= (1.085)^t

1.085(1.085)^t

t = 1 year

8.25% per year

although it didn't take the seller a year to tack on the tax

or maybe there is some time lag between collecting the sales tax and paying the government the tax

income taxes are paid yearly, but they have withholding,with penalties for underwithholding.

Maybe sales taxes are similar?

sometimes the problem is figuring out what the problem is