about give the answer cor.to..

The line that "if x=11.723456, x=12(cor.to the nearest half year)".
Is it correct? I also think that x=11.5, because 11.25<=x<11.75 will give x=11.5 (correct to the nearest half year).
For x=12(cor. to the nearest half year), the range of x should be 11.75<=x<
12.25.

2010-10-14 09:54:39 補充：
For the case of correct to the nearest year, your answers should be integers such as 8, 9, 10, 11, ...

Therefore, if the number is 11.5 or above (but less than 12.5), say 11.789, should be rounded off to
'12'.
If the number is less than 11.5, say 11.45, the rounded value should be rounded off to '11'.
Here are more examples:
11.49999 = 11 (correct to the nearest year)
11.50001 = 12 (correct to the nearest year)
11.40999 = 11 (correct to the nearest year)

So, the statement "x=11.5 or higher (but less than 12.5), then x=12" is correct.====================================================================For the case of correct to the nearest half year, your answers should be 11.5, 12.0, 12.5, 13.0, 13.5, 14.0, 14.5, ...

In your example,
if x=11.723456
x=12 (cor.to the nearest half year)

Since 11.25≤x<11.75, I think x=11.5 (cor.to the nearest half year) rather than 12.

x=11.523456
Since 11.25≤x<11.75, x=11.5 (cor.to the nearest half year)

x=11.323456
Since 11.25≤x<11.75, x=11.5 (cor.to the nearest half year)

So, if x=11.75 or higher, then x=12.

====================================================================If you have any questions, please feel free to ask.
Thank you very much!

2010-10-14 22:05:39 補充：
I think the answer is 12.
8000(1+3%)^n = 16000
n = 23.44977225
I think you should round 'up' your answer to n = 24 i.e. 12 years.
Because if you use n = 11.5, 8000(1+3%)^23 = 15788.69209 < 16000 and
n = 12, 8000(1+3%)^24 = 16262.35285 > 16000.

2010-10-14 22:06:01 補充：
Note that this kind of question is not a round 'off' question, it should be a round 'up' question instead.
If you still have questions, please feel free to ask.
Thank you very much!

2010-10-15 03:17:55 補充：
A sum of $8000 is deposited in a bank at an interest rate of 3% p.a. compounded yearly. How long will it take the money to be doubled?
Ans = 23.44977225 => 24 years (round up to the nearest year)
Ans = 23.44977225 => 23.5 years (round up to the nearest half year)

2010-10-15 03:18:32 補充：
Please feel free to ask if you still have questions.
Thank you very much!