Gah so confused...

[Comma]

In The 2006 VCAA paper, Business Maths, Q1.b.iii. The value of a machine depreciates on the reducing balance method.

if at THE END of which year will the machine's value first fall below $12000?

I got an answer of 9.9 years, which I assumed was at the END of the 9th year. However, the answers say 10 years. I'm not sure how they can say that, because wouldn't that then be at the end of 10 years, which is way past 9.9? Or am I making this too complicated and you're just supposed to round to the nearest year?

Any help would be much appreciated

[lolaser]

If you think about it, you are solving for the point at which the machine costs 12000 and then you just say at the end of that year. Therefore you always, always have to round up. As at 9.9 the machine cost 12000, not at 9, so at the end of the 9th year it still cost more than 12000.

Even if the answer came out as 9.00000001, you would say at the end of the 10th year, but VCAA will always make it like .9 or .4 or something to try and trick you.

If it says during which year btw, you also say 10th.

[tea.squaredd]

Took me a while to figure out when I was doing this. The next morning I woke up and was like.... gotta figure it out and it clicked

You have to know that in one of the question stems, it mentions that it is calculated at THE END OF THE YEAR.

Hence, when you sub. t=1 into the equation, you are calculating the amount at the END of the first year.

To understand properly:

When you sub in i.e. t= 1.2, you are calculating 0.2 into the SECOND YEAR.
same as t=3.4, you are calculating 0.4 into the FOURTH year, as t=3 is the end of the third year.

Hence when the answer says t= 9.9, it is the end of 9 years + 0.9 into the 10th year.
Thus, it will be at the END of the 10th year when you reach it, because it's all calculated at the end of the year.

[Natters]

im pretty sure its like this;
if you solved it and got 0.9, then its the end of the first year
1.9 is the end of the second year
2.9 is the end of the third year
thus 9.9 would be the end of the 10th year