偉洪淼淼@Yahoo: 2007

2007-11-18

七十二法則

迎來投資大熱，不少財經書刊都提及「七十二法則」，即

資產翻一翻所需年期　＝　７２ ÷ 年回報率
例如投資回報率為每年10%，那麼 100元在 72/10 = 7.2年便可變成200元。
由於財經書沒有解釋法則的來源，我便翻開ｎ年前的中學數學書自己計算如下：

複式利率　（１＋ｒ％）^ｎ　＝　２

其中ｒ％為年回報率；ｎ為年期
兩邊用natural log

ｌｎ（１＋ｒ％）^ｎ＝２

ｎ‧ｌｎ（１＋ｒ％）＝ｌｎ（２）＝０．６９
參考公式：

ln(1+x) = x - x²/2 + x³/3 ...

當 x << 1

ln(1+x) ≅ x
所以

　ｎ‧ｌｎ（１＋ｒ％）＝ｎ‧ｒ／１００＝０．６９

即：　ｎｒ＝６９
奇怪，這變成了６９法則！
再用試算表運算誤差如下：

原來７２法則是修正了一般ｒ由６至１２％的誤差。這區域是以往一般的回報率。

2007-10-14

A cheap upgrade project to my Canon PowerShot A610

我的Canon A610平價升級計劃
Frankly speaking, though my Canon A610 digital camera is a little bit out-dated, I enjoy very much using it for photo shooting. I particularly like the following features:

rotating LCD view finder

availability of pure manual mode (Shutter speed and Aperture)

selectable output power for the built-in flash

ergonomic hand grip

However, I do have a wish list

a wider focal length than the current 35mm

a brighter flash (especially when I need to take in-door photo, because the lens are not wide enough, I need to stand far behind and the flash will then be not strong enough)

Buying a brand-new camera (for instance, a low-end SLR) may be a choice. But since my A610 is still working well, I prefer to upgrade it. Canon does have some official accessories as follows: HF-DC1 External slave flash WC-DC56N Wide Converter (0.7X) Lens (together with the LA-DC58F Adapter)

But I don't like the idea because (1) these official upgrade will cost me the money to buy a prosumer-grade camera (2) I have already an old flash (SunPak 355AF) left for my non-digital Canon camera. This flash units support tilting and there I can set a bouncing flash. (3) My have already some lens accessories (e.g. polarizer) at 52mm mount from my bold non-digital camera. The LA-DC58F Adapter set the mount thread at 58mm and makes my original lens accessories useless.

Therefore I start to source some unofficial accessories. First I went to the AV shops and surfed internet (e.g. eBay). I do find there are some unofficial accessories for my canon A610. For instance, a 0.5X lens with adapter costs around HK$500. Okay! This meets my budget. Then, I also went to Apliu Street (鴨寮街) in Sham Shui Po. It is famous for cheap electronics/AV products, particularly when there are shops (opened in recent years) dedicated to sell products/parts from mainland China. Therefore I hope I may get some surprising cheap alternatives.

I achieved to find what I wanted, with a price below my original budget. I bought the following items:

Synchro Shoe from Y.J Photo (上海永江影視 http://www.shyj.com.cn) (HK$45)

Aluminum mount (HK$58) to physically fix the external flash with the camera

52mm Lens adapter from Fu Sen (HK$55)

Tama SRW-05 52mm 0.5X Wide converter (with macro) (HK$330) (product details at http://www.protama.com.hk/Product_ConversionLensWide.htm)

The following is the final appearance of my upgrade camera set.

Remark: the final picture is taken by the camera of my mobile phone. The quality is really bad. However, I do not have another camera.

There is some sharing after my upgrade.

Since I know the red-eye pre-flash will fool the slave flash, I have already disabled the red-eye reduction. However, when I try to my slave flash with A610 in any auto modes, although the slave flash does fire, the picture is not brighter at all. I need to resort to pure manual mode to use the slave flash (Fortunately I do have some basic photography skills to set the Shutter speed and Aperture for photo taking with flash.) After some findings at Internet, something says that the Automatic-White-Balance feature will make the built-in flash to make another pre-flash and it cannot be disabled. Anything I cannot prove this point.

The effect of bouncing flash is really good. I have attended a gathering and taken photos using it. Comparing other latest models of digital cameras from my friends (but with their built-in flashes) on the same scenario, I am proud to say the photo quality of mine is the best.