# Growth Rate Formula? (County Tax Assessor spent $4,546,431 from the counties' general fund.) #### JustinZ ##### New member In 2017, the County Tax Assessor spent$4,546,431 from the counties' general fund. In 2018, they spent $5,823,399. In 2019 they propose to spend$6,015,301. What is the annual rate of growth in the amount of funds spent by the assessor?

I know how to do it when growth rate = present - past / past x 100. I'm getting tripped up over how to work in the propose amount.

#### tkhunny

##### Moderator
Staff member
Why is it ANY different from the calculation of the 2017-2018 Growth Rate?

BTW

present - past / past x 100 MEANS $$\displaystyle present - \dfrac{past}{past}\cdot 100 = present - 1\cdot 100 = present - 100$$.

Are you SURE that's what you want?

Use parentheses to clarify meaning. (present - past) / past x 100

#### JustinZ

##### New member
Why is it ANY different from the calculation of the 2017-2018 Growth Rate?

BTW

present - past / past x 100 MEANS $$\displaystyle present - \dfrac{past}{past}\cdot 100 = present - 1\cdot 100 = present - 100$$.

Are you SURE that's what you want?

Use parentheses to clarify meaning. (present - past) / past x 100
Sorry for the confusion. The formula I was using is (Present) - (Past) / (Past) x 100. I guess my question is, how does 6,015,301 tie into all of this? That's where I'm getting lost.

#### tkhunny

##### Moderator
Staff member
1) I failed to describe adequately that notation problem. You need (Present - Past). Neither "present - past" nor "(present)-(past)" does you any good.

2) How did you calculate the 2017-2018 growth rate? Do the 2019-2018 growth rate in EXACTLY the same way.

#### Dr.Peterson

In 2017, the County Tax Assessor spent $4,546,431 from the counties' general fund. In 2018, they spent$5,823,399. In 2019 they propose to spend $6,015,301. What is the annual rate of growth in the amount of funds spent by the assessor? I know how to do it when growth rate = (present - past) / past x 100. I'm getting tripped up over how to work in the propose amount. Here's my take on the problem: There is a rate of growth from 2017 to 2018, and there is a proposed rate of growth from 2018 to 2019. They are (very) different. The question asks for one rate, namely "in the amount of funds spent" - not in the amount proposed to be spent, which has not actually been spent. So I think the 2017-2018 rate is all they are asking for. If that's not what was intended, I'm not sure what is. I presume you quoted the problem exactly and completely? #### Denis ##### Senior Member In 2017, the County Tax Assessor spent$4,546,431 from the counties' general fund. In 2018, they spent $5,823,399. In 2019 they propose to spend$6,015,301. What is the annual rate of growth in the amount of funds spent by the assessor?
Geeshhhhh...use 4,546 and 5,823 and 6,015 !!

#### JustinZ

##### New member
Geeshhhhh...use 4,546 and 5,823 and 6,015 !!
I have no idea what you're trying to say. Sorry.

#### JustinZ

##### New member
Here's my take on the problem: There is a rate of growth from 2017 to 2018, and there is a proposed rate of growth from 2018 to 2019. They are (very) different. The question asks for one rate, namely "in the amount of funds spent" - not in the amount proposed to be spent, which has not actually been spent. So I think the 2017-2018 rate is all they are asking for. If that's not what was intended, I'm not sure what is.

I presume you quoted the problem exactly and completely?
Yes, I quoted it exactly how he gave it to us. He did give us four possible answer choices:

#### HallsofIvy

##### Elite Member
Which growth rate do you want to calculate?

The growth rate from 2017 to 2018 was (5283399- 4546431)/4546431= 16.2%.
The growth rate from 2018 to 2019 will be (6015301- 5283399)/5283399= 13.8%.
The growth rate from 2017 to 2019 will be (6015301- 4546431)/4546431= 32.3%. In this last case, the annual growth rate will be 32.3/2= 16.15%.

#### Denis

##### Senior Member
Disagree.
4546431(1 + r)^2 = 6015301 : r = .150253.....or ~15%