# Thread: Tax Rate changes after sometime, how to find it?

1. ## Tax Rate changes after sometime, how to find it?

Hi,

I've been trying to solve the following problem:

A seller deposited $8.000, 1 year and 4 months after, he raised$8.480.
Knowing that, some time after the deposite, the anual tax rate passed from 4% to 6%, determinate how much time it took for the tax change to happen ?

This is what I've tryed (and a couple of 3 diferent methods, similar to this one):

I know that, 8.480 = 8.000(1 + 16/12 * i)

Interest = i

so, I wrote the following equation for the given word problem

( i1 + i2 ) + c1 = c1( 1 + 16/12 * i )

I started by finding i wish gives me i = 0,04466 ~ 0,045

I know that,

i1 + i2 = 480 , from a total of 16 months

i1 = 8.000 + [ (16-n1)/12 ] * 0,04

i2 = 8.000 + [ (16-n2)/12 ] * 0,06

It gave me,

i1 = (320n1)/12

and

i2 = (480n2)/12

further I've picked from i1 + i2 = 480

the following result,

[(320n1)/12] + [(480n2)/12] = 480

n1 = 216 - 480n2

I was thinking that, if I used this values I could get the answer by

(8.000 * [(216-480n2)/12] * 0,04) + (8000 * (n2/12) * 0,06) + 8.000 = 8.480

But it does not... probably I've got lots of errors and I'm not that good in math, but I do my best

Any sugestion is appreciated!

2. I've tryed it a couple of times more, without success.

Unfortunately the steps above, that I pasted have lots of errors, but the way is done or I've used is that one

3. Originally Posted by heldrida
A seller deposited $8.000, 1 year and 4 months after, he raised$8.480.
Knowing that, some time after the deposite, the anual tax rate passed from 4% to 6% .....
In future:
Please post (as example) $8.000 this way:$8,000
Please use INTEREST rate, not tax rate.
Please use CHANGED (not passed) and ACCUMULATED (not raised).

Here's a much simpler way:
t = time = 1+1/3 year = 4/3 year
x = time at 4%

8000(.04x) + 8000(.06(4/3 - x)) = 480
.04x + .06(4/3 - x) = 480/8000

I'm sure you can finish it