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标题: Reading 5: The Time Value of Money-LOS c习题精选 [打印本页]
作者: bmaggie    时间: 2010-4-6 14:36     标题: [2010]Session 2:-Reading 5: The Time Value of Money-LOS c习题精选

A local bank offers an account that pays 8%, compounded quarterly, for any deposits of $10,000 or more that are left in the account for a period of 5 years. The effective annual rate of interest on this account is:

A)
 8.24%.
B)
 4.65%.
C)
 9.01%.


(1 + periodic rate)m ? 1 = (1.02)4 ? 1 = 8.24%.

作者: bmaggie    时间: 2010-4-6 14:36

Which of the following is the most accurate statement about stated and effective annual interest rates?

A)
 The stated rate adjusts for the frequency of compounding.
B)
 The stated annual interest rate is used to find the effective annual rate.
C)
 So long as interest is compounded more than once a year, the stated annual rate will always be more than the effective rate.


The effective annual rate, not the stated rate, adjusts for the frequency of compounding. The nominal, stated, and stated annual rates are all the same thing.

作者: bmaggie    时间: 2010-4-6 14:36

A major brokerage house is currently selling an investment product that offers an 8% rate of return, compounded monthly. Based on this information, it follows that this investment has:

A)
 a periodic interest rate of 0.667%.
B)
 an effective annual rate of 8.00%.
C)
 a stated rate of 0.830%.


Periodic rate = 8.0 / 12 = 0.667. Stated rate is 8.0% and effective rate is 8.30%.

作者: bmaggie    时间: 2010-4-6 14:37

Use a stated rate of 9% compounded periodically to answer the following three questions. Select the choice that is the closest to the correct answer.

The semi-annual effective rate is:

A)
 9.00%.
B)
 9.31%.
C)
 9.20%.


First, we need to calculate the periodic rate, or 0.09 / 2 = 0.045.

Then, the effective semi-annual rate = (1 + 0.045)2 ? 1 = 0.09203, or 9.20%.

The quarterly effective rate is:

A)
 9.31%.
B)
 9.40%.
C)
 9.00%.

First, we need to calculate the periodic rate, or 0.09 / 4 = 0.0225.

Then, the effective annual rate = (1 + 0.0225)4 ? 1 = 0.09308, or 9.31%.

The continuously compounded rate is:

A)
 9.42%.
B)
 9.67%.
C)
 9.20%.


The continuously compounded rate = er ? 1 = e0.09 ? 1 = 0.09417, or 9.42%.

Calculator Keystrokes for et: Using the TI BA, enter [0.09] [2nd] [ex] (this is the key with LN on the face of the button). On the HP, enter [0.09] [g] [ex] (this key is located in blue on the key with 1/x in white print).

作者: bmaggie    时间: 2010-4-6 14:37

What’s the effective rate of return on an investment that generates a return of 12%, compounded quarterly?

A)
 14.34%.
B)
 12.00%.
C)
 12.55%.


(1 + 0.12 / 4)4 ? 1 = 1.1255 ? 1 = 0.1255.

作者: bmaggie    时间: 2010-4-6 14:37

Peter Wallace wants to deposit $10,000 in a bank certificate of deposit (CD). Wallace is considering the following banks: 

Which bank offers the highest effective interest rate and how much?

A)
 Bank A, 5.85%.
B)
 Bank B, 5.90%.
C)
 Bank C, 5.87%.


Effective interest rates:

Bank A = 5.85 (already annual compounding)

Bank B, nominal = 5.75; C/Y = 12; effective = 5.90

Bank C, nominal = 5.70, C/Y = 365; effective = 5.87

Hence Bank B has the highest effective interest rate.

作者: bmaggie    时间: 2010-4-6 14:38

A local loan shark offers 4 for 5 on payday. What it involves is that you borrow $4 from him and repay $5 on the next payday (one week later). What would the stated annual interest rate be on this loan, with weekly compounding? Assuming 52 weeks in one year, what is the effective annual interest rate on this loan? Select the respective answer choices closest to your numbers.

A)
 25%; 1,300%.
B)
 1,300%; 10,947,544%.
C)
 25%; 300%.


Stated Weekly Rate= 5/4 ? 1 = 25%
Stated Annual Rate = 1,300%

Annual Effective Interest Rate = (1 + 0.25)52 ? 1 = 109,476.44 ? 1 = 10,947,544%

作者: bmaggie    时间: 2010-4-6 14:38

What is the effective annual rate if the stated rate is 12% compounded quarterly?

A)
 57.35%.
B)
 12.55%.
C)
 12.00%.


EAR = (1 + 0.12 / 4)4 – 1 = 12.55%

作者: bmaggie    时间: 2010-4-6 14:38

As the number of compounding periods increases, what is the effect on the annual percentage rate (APR) and the effective annual rate (EAR)?

A)
 APR increases, EAR increases.
B)
 APR remains the same, EAR increases.
C)
 APR increases, EAR remains the same.


The APR remains the same since the APR is computed as (interest per period) × (number of compounding periods in 1 year). As the frequency of compounding increases, the interest rate per period decreases leaving the original APR unchanged. However, the EAR increases with the frequency of compounding.

作者: bmaggie    时间: 2010-4-6 14:38

A local bank advertises that it will pay interest at the rate of 4.5%, compounded monthly, on regular savings accounts. What is the effective rate of interest that the bank is paying on these accounts?

A)
 4.65%.
B)
 4.59%.
C)
 4.50%.


(1 + 0.045 / 12)12 ? 1 = 1.0459 ? 1 = 0.0459.

作者: bmaggie    时间: 2010-4-6 14:38

As the number of compounding periods increases, what is the effect on the EAR? EAR:

A)
 increases at an increasing rate.
B)
 does not increase.
C)
 increases at a decreasing rate.


There is an upper limit to the EAR as the frequency of compounding increases. In the limit, with continuous compounding the EAR = eAPR –1. Hence, the EAR increases at a decreasing rate.

作者: zaestau    时间: 2010-4-25 00:08

 c
作者: kison    时间: 2010-8-23 21:48

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