求助一道财管题~（200论坛币）

银行向你提供年利率为7.06%的7个月期存单，该存单的实际年收益率为7.25%。 对于7个月期的存单，利息是按1天、1周、1个月和1个季度中哪一个计算的？如果将10000元存成这种存单，在7个月后存单到期时，你将获得多少钱？即在第7个月月末，如果你结清存款账户，那么银行将给你多少钱？请给出详细解答

（ps 一年按365天算 一月按30天算 一周按7天算）

帮你顶起来

就没一个会的么？

你要把假设写全。
convention是什么？一年按多少天算？有没有大小月？如果有大小月，是那七个月?
因为按天和月算设计到这些conventions.

顶起来啊~

我急需知道答案啊~

{:soso_e100:}{:soso_e100:}

D.L 发表于 2013-9-7 11:34

你不回答我要求的补充假设没法算

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

(1+ 7.06%/x)^x =1+ 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.

-------------------------------------------------
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.

see my answer on the 8th floor.