Quantitative Methods 【Reading 5】Sample default, following, one, statements

karoliukas

Which one of the following statements best describes the components of the required interest rate on a security?

A) The nominal risk-free rate, the expected inflation rate, the default risk premium, a liquidity premium and a premium to reflect the risk associated with the maturity of the security.

B) The real risk-free rate, the default risk premium, a liquidity premium and a premium to reflect the risk associated with the maturity of the security.

C) The real risk-free rate, the expected inflation rate, the default risk premium, a liquidity premium and a premium to reflect the risk associated with the maturity of the security.

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The required interest rate on a security is made up of the nominal rate which is in turn made up of the real risk-free rate plus the expected inflation rate. It should also contain a liquidity premium as well as a premium related to the maturity of the security.

karoliukas

T-bill yields can be thought of as:

A) nominal risk-free rates because they contain an inflation premium.

B) nominal risk-free rates because they do not contain an inflation premium.

C) real risk-free rates because they contain an inflation premium.

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T-bills are government issued securities and are therefore considered to be default risk free. More precisely, they are nominal risk-free rates rather than real risk-free rates since they contain a premium for expected inflation.

karoliukas

The real risk-free rate can be thought of as:

A) exactly the nominal risk-free rate reduced by the expected inflation rate.

B) approximately the nominal risk-free rate reduced by the expected inflation rate.

C) approximately the nominal risk-free rate plus the expected inflation rate.

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The approximate relationship between nominal rates, real rates and expected inflation rates can be written as:

Nominal risk-free rate = real risk-free rate + expected inflation rate.

Therefore we can rewrite this equation in terms of the real risk-free rate as:

Real risk-free rate = Nominal risk-free rate – expected inflation rate

The exact relation is: (1 + real)(1 + expected inflation) = (1 + nominal)

karoliukas

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) 4.65%.

B) 9.01%.

C) 8.24%.

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

karoliukas

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) So long as interest is compounded more than once a year, the stated annual rate will always be more than the effective rate.

C) The stated annual interest rate is used to find the effective annual rate.

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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.

karoliukas

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) an effective annual rate of 8.00%.

B) a periodic interest rate of 0.667%.

C) a stated rate of 0.830%.

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

karoliukas

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) 9.20%.

C) 9.31%.

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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%.

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The quarterly effective rate is:

A) 9.40%.

B) 9.00%.

C) 9.31%.

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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%.

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The continuously compounded rate is:

A) 9.67%.

B) 9.20%.

C) 9.42%.

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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).

karoliukas

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

A) 12.55%.

B) 14.34%.

C) 12.00%.

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

karoliukas

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

• Bank A offers 5.85% annual interest compounded annually.
• Bank B offers 5.75% annual interest rate compounded monthly.
• Bank C offers 5.70% annual interest compounded daily.

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

A) Bank A, 5.85%.

B) Bank C, 5.87%.

C) Bank B, 5.90%.

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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.

karoliukas

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) 25%; 300%.

C) 1,300%; 10,947,544%.

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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%