tax collector and thief

[perki]

Hello, I've got the following problem. There is a tax collector in the kingdom, and there is a thief who steals from the tax collector. Due to the thief's thieving, we know that tax collectors revenues have been decreasing by 12% annually, and this amount represents thief's revenues. We assume that the total taxes collected remain constant, the only thing that changes is that each year the tax collector is losing 12% compared to the previous year (declining revenue), and that amount is taken by the thief. The tax collectors revenue for this year is 1,500,000 euros.

The problem sounds simple but I'm not getting the numbers I want. The table below is what I got so far. The current year is 0 and there are past 3 years. Basically I want to calculate the revenue decline of tax collector and revenue increase of the thief for the past 3 years.

I assumed that for this year 1,500,000 is 88% of Tax collectors revenues of previous year, because it is a 12% decline, so I did 1,500.000/0.88 and did that for each previous year.

Year	-3	-2	-1	0
Tax collector revenues	2201117.58	1936983.47	1704545.45	1,500,000
Thief revenues
Total revenues				const.

After this I am stuck because I don't see how to calculate thief's revenues, and the total revenues which I know are constant and are zero sum.

 

[perki]

Your problem makes no sense...
If collections remain constant, then the 1,500,000 remains constant,
and the thief gets 1500000*.12 = 180,000 each year, so 1,320,000
remains for the collector.

If you're learning Present and Future values, and your teacher
is looking for the future value of 1500000 over 3 years @ 12%
annually (then your teacher should be shot at sunrise for making
up that silly problem!); future value would be 1500000*1.12^3 = 2107392.

Okay thank you!