Reading 5: The Time Value of Money-LOS c习题精选 2011, effective, frequency, interpret, deposits

1215

Session 2: Quantitative Methods: Basic Concepts
Reading 5: The Time Value of Money

LOS c: Calculate and interpret the effective annual rate, given the stated annual interest rate and the frequency of compounding.

 

 

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%.

1215

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

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

B) The stated rate adjusts for the frequency of compounding.

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.

1215

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 stated rate of 0.830%.

C) a periodic interest rate of 0.667%.

---

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

1215

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%.

---

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) 9.40%.

B) 9.31%.

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) 9.67%.

B) 9.20%.

C) 9.42%.

---

The continuously compounded rate = e^r ? 1 = e^0.09 ? 1 = 0.09417, or 9.42%.

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

1215

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%.

---

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

1215

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 B, 5.90%.

B) Bank A, 5.85%.

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.

1215

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%

1215

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

A) 12.55%.

B) 57.35%.

C) 12.00%.

---

EAR = (1 + 0.12 / 4)⁴ – 1 = 12.55%

1215

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.

1215

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.