求助一道财管题~（200论坛币）

sunnywu72 发表于 2013-9-7 14:16
This is really simple.
Let's say the compounding frequency is x, mathematically, we have

同意你的做法，其实这个问题分成两步解决：
1，找出计算实际年收益率使用的复利期间；是按日，周，季度还是年；  简单而言
（1+r/n)^n=R   名义利率r;实际利率R; n代表复利次数，进而推算出计息周期；
2，按照找到的复利次数得出的计息周期计算应获得本期收益：本金+利息
公式有两个 ，可互换
自然对数公式e^rT;或者刚才提到的公式
给楼主奖金吧

This is really simple.
Let's say the compounding frequency is x, mathematically, we have

(1+ 7.06%/x)^x = 7.25%. Solve for x, which should be one of 4, 12, 52, or 365, corresponding to quarterly, monthly, weekly or daily compounding frequency, respectively. This equation cannot be solved for a closed form solution since it is not a normal function. However, we can still solve it either numerically or by trial and error.

To simplify the calculation, we could take the natural log on both sides and change the equation to its equivalent,
x*ln(1+7.06%/x) = ln(1+7.25%).

Using MS Excel, we have the following results,

compounding  frequency  natural log of gross  annualized interest rate (lefthand side)  natural log of gross interest rate(righthand side)
Quarterly (x=4)
0.06998419
0.069992372

Monthly (x=12)
0.070393129

0.069992372

weekly (x=52)
0.070552117

0.069992372

Daily (x=365)
0.070593173

0.069992372






Number of  quarters
7/3

2.333333333

Initial  deposit
10000




10000*(1+7.06%/4)^2.33333
=
10416.68871



We can see the quarterly compounding frequency leads to the annualized interest rate closest to the given one.
So we should use quarterly compounding.

The intesest the investor will receive 7 months later is 416.69 Yuan, rounding to Fen. Taking the principal into account,the bank will give 10416.69 Yuan in total back to the investor.

wxfwolf 发表于 2013-9-7 17:04
同意你的做法，其实这个问题分成两步解决：
1，找出计算实际年收益率使用的复利期间；是按日，周，季度还 ...

e^(r*T) is not relevant to the current scenario. That formula is for continuous compounding, which implies the compounding frequency is infinitely large, neither daily, weekly, monthly, quarterly, nor yearly. If we compound the initial deposit continuously , the terminal value is larger than any other that employs discrete-time compounding frequency.

NOTE: On the third line, one (1) was missing on the righthand side of the equality. I already added it to make the answer accurate. The remaining part is typo-free.

哥们，至于第二个公式e^rT麻烦你用点数学，特别是积分知识，哎呀，我就不说了，不懂看看金融数学相关章节。任何事情，尽可能简化是事件处置的方向。 交个朋友呗，髙名几何，是否姓吴，武……

D.L 发表于 2013-9-7 11:32
我急需知道答案啊~

哥们，sunnywu72的回答就是对的，你不会看不懂英文吧。具体步骤：
1，推算一个年度的复利次数  (1+r/n)^n-1=R  r 名义利率或票面利率；n 复利次数/年；R 实际利率；
2，根据n推算复利周期；像本例题就是季度；
3，如果本金为C，到期日本金利息和就是  C*（1+r/n)^(7/3);
注释：可能对你对复利公式存在疑问，在公式*（1+r/n)^(7/3)中使用的名义利率r/n与计息周期（7/3）是对应关系，在本例中7个月相当于本金利息复利了2.33次

wxfwolf 发表于 2013-9-10 11:47
哥们，至于第二个公式e^rT麻烦你用点数学，特别是积分知识，哎呀，我就不说了，不懂看看金融数学相关章节。 ...

I have to say again what you are talking about is irrelevant. Please allow me to emphasize that I am not saying the formula does not exist. Neither do I say the formula is wrong. However, only if x goes infinity, the discrete-time formula becomes e^(r*T). Unfortunately,  only the discrete-time formula is relevant to the question. You don't have to show off how many finance books you have read because that implies you are sure how many finance books I have crammed.

By the way, why I responded to your post is you said

"公式有两个 ，可互换 自然对数公式e^rT"   They are applied to differenct settings and NOT interchangeable unless you are implied or explicitly asked to use one in lieu of another.

啊啊啊啊啊啊啊啊啊

楼主在问题中没有说明计息期。若计息期为1个月，则到期本利和为10419元；若与银行协商好计息期为7个月，则到期本利和为10411.83元。详细计算过程见附件。

我想楼主该到时间给我论坛币了吧？ 我可是遵照版规跟帖回复，给出详细答案，而不是以购买方式。希望生活在一个信用世界。