- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 1. The Time Value of Money
- Subject 6. Calculate the Effective Annual Rate

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**CFA Practice Question**

The new products officer for the Strong-n-Safe Bank is trying to determine the stated rate for a new 4 year CD. The effective rate will be 6.95% and the CD will offer continuous compounding. The advertised stated rate would be closest to ______.

B. 6.82%

C. 7.20%

A. 6.72%

B. 6.82%

C. 7.20%

Correct Answer: A

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**User Contributed Comments**
35

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

tawi |
How did they get that? |

tawi |
Ok I got it ! The formula for Eff. Ann. Rate is EAR= e^r -1 |

brimann |
Using the interest conversion capabilities of the BAII+ I used the continuous compounding fuction on 12 which = 162,754 and plugged that in for C/Y, EFF = 6.95 then CPT NOM = 6.7191 |

KD101 |
Brimann's idea is good. Here are the step by step Hit 2nd - [ICONV] See NOM - Hit Down Arrow See EFF - Hit 6.95 See C/Y - Hit 12 then 2nd[e^X] and hit ENTER Now Down Arrow Key Now when you see NOM - Hit CPT You get 6.7191 |

gruszewski |
By the way KD101, C/Y can be any large number, why making it more difficult than it is with this e^X :-) |

gruszewski |
the fastest way is ln(1.0695) |

Hamma |
Thus is this the formula then? EAR(continuous compounding)= e^r - 1 0.0695 = e^r - 1 ln(1.0695)=r |

debby2 |
stated interest rate = ln (1+EAR) |

Will1868 |
debby2 is smart |

MARINGI |
gruszewski. thats pretty fast |

Win1977 |
Still confused on this one, could someone explain it based on using the BAII calc? Thanks. |

0is4eva |
Recall that: FV(N) = PV * (1 + EAR)^N = PV * e^(r * N) r is the stated annual rate, EAR = effective annual rate. Abbreviate formula, recall that N=1, and solve for r: (1 + EAR) = e^(r) ln(1 + EAR) = ln( e^(r) ) ln(1 + EAR) = r ln(1.0695) = r r = 0.06719 = 6.72% |

Cooltallgal |
What C/Y is 12? The question only mentioned 4 years compound, but didn't say its compounding monthly... |

faya |
e^r-1 results in compounded return = 0.0695 To 'un-compound', take logs - ie. ln(1+r) = ln(1.0695) = 0.06719 as Ois4eva says. |

gizi |
Using BA11 Plus: 2nd ICONV 2nd CLR WORK EFF = 6.95 C/Y = 365 (365 dys in yr) CPT NOM = 6.719 |

Kofo |
pls: can someone say how to do this using the HP12C |

AndressaS |
Here you go using HP12C: 6.95 ENTER 100 % 1 + g LN Total: 0.06719 x 100 = 6.72% |

StanleyMo |
it has mentioned continuous compounding, so the formula use would be EAR = E^Rs-1 |

kamil1 |
in HP (1+0.0695)ln Than just multiply by 100 to get rid of the rounding |

ravdo |
When I do it exactly the way suggested by AndressaS and kamil1, my answer turns out to be 2.07. What am I doing wrong? Please take it step by step with the HP12C calc |

TammTamm |
Thanks debby2, the way you explained this appears to be the easiest way to remember it. |

JKiro |
note debby2 "formula" is for continous compounding |

gazelle |
ravdo, If you are using the ALG Mode,try those following steps: 6.95[%] +1[ENTER] [G][LN] = 0.6719 X 100= 6.72% |

mwali |
Hi Gizi: your method is straight forward. Thanx |

SANTOSHPRABHU |
STATED INTEREST RATE = ln (1 + EAR) = ln (1+0.0695)= 0.0671912 X 100 = 6.72% (4 year CD is an additional information and will not effect in our calculation of Stated Int Rate) |

pokigbo |
HP 12c Platinum 1 ENTER 0.0695 [+] [g][LN] 0.067191 100 [x] 6.72 |

hussein1978 |
what is cd |

vatsal92 |
Corporate Deposits |

deliawmx |
CD means certificate of deposit. |

Yrazzaq88 |
Use this in your texas instruments ICONV Effective interest = 6.95% C/Y = 48 (4 years) Nom = CPT =6.72 |

Chl4072 |
1.0695 [LN] Finally get the answer!!! |

marianne19 |
see irazaaq for computation 4 years to 12 months = 48 months |

nohuchi |
EAR(continuous compounding)= e^r - 1 2nd ICONV 2nd CLR WORK EFF = 6.95 C/Y = 365 (365 dys in yr) CPT NOM = 6.719 |

abs013 |
There's too many different ways in the comment section. 2nd ICONV 2nd CLR WORK EFF = 6.95 C/Y = 12*4 = 48 CMPT NOM = 6.72 |

anthealing |
[2nd][ICONV] [2nd][CLR WORK] [EFF]=6.95 [C/Y]=1,000,000,000 (means e) ]NOM][CPT]=6.719 |