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A bank quote  certificate of deposit (CD) yields both as annual percentage
rates(APR),without compounding and as annual percentage yields(APY) that
include the effects of monthly compounding.A $100,000 CD will pay $110,471.31
at the end of the year.Calculate the APR and APY the bank is quoting.
答案：
For APR,PV=100,000;FV=-110,471.31;PMT=0;N=12，CPT I/Y=0.8333， which is the
monthly rate. The ARP=12*0.8333,算出APR=10%
For APY,APY=(110,471.31/100,000)-1=10.471%
这里我不明白，为什么APY是直接算出来的，我和答案的算法刚好相反，是我把题目理解错
了么？各位大侠帮忙回答一下，谢谢了！


我看了一下人大经济论坛上给出的解释：大意是APR是nominal rate,所以0.8333*12可得

ARY是EAR ( effective annual rate 有效年利率)所以 用（1+10%/12)的12次方-1也可得
出10.471这个答案

但是我不理解的是，书上在给出计算过程以后，来了这么一句：

note that the APY, which includes the effects of compounding, must logically
be larger than the APR, which does not.

那这题如果答案正确，APY>APR，怎么破？

说的比较多，不知道看上去乱不乱了，望大牛解答，谢谢啦

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关键词：CFA 计算题 compounding Certificate percentage percentage deposit include

没看懂。。。

APY>APR 然后你的问题是？

elishjkl 发表于 2013-1-28 12:57
APY>APR 然后你的问题是？

我的问题是 教材里说的这句话： note that the APY, which includes the effects of compounding, must logically  be larger than the APR, which does not.
意思不就是：通常我们认为APY应该比APR大，其实不是。是在suggest APY <APR啊

APR-Stated annual rateAPY-Effective annual rate

那么就存在关系(1+APR/12)^12-1=APY
APY=10.471%
APR=10%

1. 但是我不理解的是，书上在给出计算过程以后，来了这么一句：
   
2. 
   
3. note that the APY, which includes the effects of compounding, must logically
   
4. be larger than the APR, which does not.

复制代码

关于这个不必太较真，一般APY是会大于APR的，因为有compound 效果，

你句子理解错了  后面从句修饰APR的 不是之前的整句话

这句话意思应该是
note that the APY（which includes the effects of compounding）must logically  be larger than the APR（which does not include the effects of compounding）.

including the effects of monthly compounding, implying that APY=Effective annual rate. feel free to use compouding equition (1+APY)^(1/m) to get effective periodic rate.
with out compounding effects, which means APR=YTM. effective periodical rate=APR/m. You cannot use the above equition to tranfer APR into periodical rate. After you compute the value of periodic rate, the only way obtaining APR is timing the value by m, the number of compouding period. very similar to YTM.

generally, when compouding frequency increases, the EAR(APR) increases as well.