- CFA Exams
- CFA Level I Exam
- Study Session 2. Quantitative Methods (1)
- Reading 6. The Time Value of Money
- Subject 2. Calculate the Effective Annual Rate

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**CFA Practice Question**

If the nominal interest rate is 7%, the effective annual rate is:

II. 7.21% with monthly compounding

III. 7.25 % with continuous compounding

I. 7.19 % with quarterly compounding

II. 7.21% with monthly compounding

III. 7.25 % with continuous compounding

Which one of the following is true?

A. I and III

B. II and III

C. I, II and III

**Explanation:**Using Texas Instruments BA II PLUS

For m = 4

2nd ICONV: NOM = previous value

2nd CLRWORK: NOM = 0.00

7 ENTER: NOM = 7.00

DownArrow: EFF = 0.00

DownArrow: C/Y = previous value

(**)4 ENTER: C/Y = 4.00

UpArrow: EFF = 0.00

CPT: EFF = 7.19

(I) is correct

Note: For n = 12, replace 4 by 12 in line (**)

Using HP 12C

For m = 12

f CLEAR REG: 0.00000000

f CLEAR FIN: 0.00000000

7 ENTER: 7.00000000

(*) 12 n divided by i: 0.58333333

100 CHS ENTER PV: - 100.00000000

FV: - 107.2290081

Divided by 12: 7.22900810

(II) is not correct

Note: For quarterly compounding, replace 12 by 4 in line (*)

For m = 8, i.e., continuous compounding:

1 ENTER: 1.00000000

7%: 0.07000000

g e

^{x}: 1.07250818

Δ%: 7.25081810

(III) is correct.

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**User Contributed Comments**
7

User |
Comment |
---|---|

aspazia |
how do you get III true on a Texas BA II Plus? thanks |

jmcneal |
Type in .07 hit the 2nd key then E^x it returns 1.07250818. Then subtract 1. |

sh21 |
Thanks jmneal! |

shiva5555 |
For III, I think the natural log is easier to remember. Ln(1-.07) = 7.25 % |

TiredHand |
Using that info I get EFF = 7.229% on monthly compouding, which is not the same as 7.21% in the answer |

TiredHand |
Got it - B is NOT THE ANSWER because the monthly compounding EAR is not 7.21% it is in fact 7.229%. I love the BAII Plus |

lordcomas |
Or type in: 1,000,000.00 ENTER: C/Y Then compute for EFF. |