LOS c, (Part 1): Calculate and interpret the effective annual rate, given the stated annual interest rate and the frequency of compounding.

1、Use a stated rate of 9 percent 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)   9.20%.

B)   9.00%.

C)   10.25%.

D)   9.31%.

A)   9.31%.

B)   9.00%.

C)   9.20%.

D)   9.40%.

A)   9.20%.

B)   9.45%.

C)   9.42%.

D)   9.67%.

A)   12.00%.

B)   12.55%.

C)   3.00%.

D)   57.35%.

A)   a stated rate of 0.830%.

B)   an effective annual rate of 8.00%.

C)   a periodic interest rate of 0.667%.

D)   a nominal effective rate of 6.67%.

答案和详解如下：

1、Use a stated rate of 9 percent 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)   9.20%.

B)   9.00%.

C)   10.25%.

D)   9.31%.

The correct answer was A)

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%.

2、The quarterly effective rate is:

A)   9.31%.

B)   9.00%.

C)   9.20%.

D)   9.40%.

The correct answer was A)

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%.

3、The continuously compounded rate is:

A)   9.20%.

B)   9.45%.

C)   9.42%.

D)   9.67%.

The correct answer was C)

The continuously compounded rate = e^r - 1 = e^.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).

4、What is the effective annual rate if the stated rate is 12 percent compounded quarterly?

A)   12.00%.

B)   12.55%.

C)   3.00%.

D)   57.35%.

The correct answer was B)     

EAR = (1 + 0.12/4)⁴ – 1 = 12.55%

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

A)   a stated rate of 0.830%.

B)   an effective annual rate of 8.00%.

C)   a periodic interest rate of 0.667%.

D)   a nominal effective rate of 6.67%.

The correct answer was

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