问一道题：NO.PZ2017092702000017

问题如下：

Given a stated annual interest rate of 6% compounded quarterly, the level amount that, deposited quarterly, will grow to £25,000 at the end of 10 years is closest to:

选项：

£461.

£474.

£836.

解释：

A is correct.

To solve for an annuity (A) payment, when the future value (FV), interest rate, and number of periods is known, use the following equation:

${l}FV=A{\lbrack\frac{{(1+\frac{r_s}m)}^{mN}-1}{\frac rm}\rbrack}\\25,000=A{\lbrack\frac{{(1+\frac{0.06}4)}^{4\times10}-1}{\frac{0.06}4}\rbrack}$

A=460.68

怎么判断什么时候需要算EAR，什么时候只需要用利率/期数？。我这题就是看到了compound quarterly,所以用之前EAR的公式算了，再把EAR作为I/Y进行计算

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1 个答案

星星_品职助教 · 2020年03月21日

同学你好，

EAR是有效“年”利率，所以如果N设定为一年为一期的情况下就要算EAR。

题干中出现“stated annual interest rate of 6% compounded quarterly”这种描述的时候，肯定要对利率做转化。因为stated annual interest rate 是无法直接计算的。区别就在于如果要设置一年为一期，就需要转化成EAR，如果设置一个季度为一期，就不用另外再转化成EAR，只算期间利率即可。期间利率和N要相互对应的上，如果期间利率用的是EAR，但N是季度数字，就错了。

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星星_品职助教 · 2020年03月22日

这个我不知道唉，可能得问一下辅导员

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NO.PZ2017092702000017问题如下Given a stateannuinterest rate of 6% compounquarterly, the level amount that, positequarterly, will grow to £25,000 the enof 10 years is closest to:A.£461.B.£474.C.£836. A is correct. To solve for annuity (payment, when the future value (FV), interest rate, annumber of perio is known, use the following equation:lFV=A[(1+rsm)mN−1rm]25,000=A[(1+0.064)4×10−10.064]{l}FV=A{\lbrack\frac{{(1+\frac{r_s}m)}^{mN}-1}{\frrm}\rbrack}\\25,000=A{\lbrack\frac{{(1+\frac{0.06}4)}^{4\times10}-1}{\frac{0.06}4}\rbrack}lFV=A[mr(1+mrs)mN−1]25,000=A[40.06(1+40.06)4×10−1]A=460.68计算器按法6%/4=1.5%。所以I/Y=1.5，N=10*4=40，FV=25000，PV=0，CPT PMT=-460.6775. 为什么I/Y用的不是EAR/4?

2023-07-20 19:25 1 · 回答

NO.PZ2017092702000017问题如下 Given a stateannuinterest rate of 6% compounquarterly, the level amount that, positequarterly, will grow to £25,000 the enof 10 years is closest to:A.£461.B.£474.C.£836. A is correct. To solve for annuity (payment, when the future value (FV), interest rate, annumber of perio is known, use the following equation:lFV=A[(1+rsm)mN−1rm]25,000=A[(1+0.064)4×10−10.064]{l}FV=A{\lbrack\frac{{(1+\frac{r_s}m)}^{mN}-1}{\frrm}\rbrack}\\25,000=A{\lbrack\frac{{(1+\frac{0.06}4)}^{4\times10}-1}{\frac{0.06}4}\rbrack}lFV=A[mr(1+mrs)mN−1]25,000=A[40.06(1+40.06)4×10−1]A=460.68计算器按法6%/4=1.5%。所以I/Y=1.5，N=10*4=40，FV=25000，PV=0，CPT PMT=-460.6775. 题目从哪里可以看出要求的是PMT

2023-06-08 19:32 1 · 回答

NO.PZ2017092702000017 问题如下 Given a stateannuinterest rate of 6% compounquarterly, the level amount that, positequarterly, will grow to £25,000 the enof 10 years is closest to: A.£461. B.£474. C.£836. A is correct. To solve for annuity (payment, when the future value (FV), interest rate, annumber of perio is known, use the following equation:lFV=A[(1+rsm)mN−1rm]25,000=A[(1+0.064)4×10−10.064]{l}FV=A{\lbrack\frac{{(1+\frac{r_s}m)}^{mN}-1}{\frrm}\rbrack}\\25,000=A{\lbrack\frac{{(1+\frac{0.06}4)}^{4\times10}-1}{\frac{0.06}4}\rbrack}lFV=A[mr(1+mrs)mN−1]25,000=A[40.06(1+40.06)4×10−1]A=460.68计算器按法6%/4=1.5%。所以I/Y=1.5，N=10*4=40，FV=25000，PV=0，CPT PMT=-460.6775. 首先我理解的题目意思是6%年化，1年4次复利，得到EAR，然后在这个EAR水平下也进行每年复利4次，10年后得到25000刀，问每年存入多少钱

2022-08-22 16:02 1 · 回答

NO.PZ2017092702000017 问题如下 Given a stateannuinterest rate of 6% compounquarterly, the level amount that, positequarterly, will grow to £25,000 the enof 10 years is closest to: A.£461. B.£474. C.£836. A is correct. To solve for annuity (payment, when the future value (FV), interest rate, annumber of perio is known, use the following equation:lFV=A[(1+rsm)mN−1rm]25,000=A[(1+0.064)4×10−10.064]{l}FV=A{\lbrack\frac{{(1+\frac{r_s}m)}^{mN}-1}{\frrm}\rbrack}\\25,000=A{\lbrack\frac{{(1+\frac{0.06}4)}^{4\times10}-1}{\frac{0.06}4}\rbrack}lFV=A[mr(1+mrs)mN−1]25,000=A[40.06(1+40.06)4×10−1]A=460.68计算器按法6%/4=1.5%。所以I/Y=1.5，N=10*4=40，FV=25000，PV=0，CPT PMT=-460.6775. 老师，为什么这道题不求EAR呢？为什么我觉得用EAR除以4，才是最终计算器要带入的1/Y呢

2022-05-08 17:48 1 · 回答

NO.PZ2017092702000017 从那句话可以推断出这道题目的PV是0呢？

2021-11-16 20:38 1 · 回答

问一道题：NO.PZ2017092702000017

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