- CFA Exams
- 2021 Level I
- Study Session 2. Quantitative Methods (1)
- Reading 6. The Time Value of Money
- Subject 2. Calculate the Effective Annual Rate

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##### Subject 2. Calculate the Effective Annual Rate PDF Download

There are three ways to quote interest rates for investments paying interest more than once a year:

The effective interest rate with quarterly compounding is 8.24%.

1. Press 2nd ICONV to select the worksheet

2. NOM will be displayed with the previous value

3. Press 2nd [CLR WORK] to clear the worksheet

2nd ICONV: NOM = previous value

2nd CLRWORK: NOM = 0.00

8 ENTER: NOM = 8.00

DownArrow: EFF = 0.00

DownArrow: C/Y = previous value

4 ENTER: C/Y = 4.00

DownArrow: EFF = 0.00

CPT: EFF = 8.24

g END: Previous value

f CLEAR FIN: 0.00000000

f CLEAR REG: 0.00000000

8 ENTER: 8.00000000

4n i 0.66666667

100 CHS PV: -100.00000000

FV: 108.2432160

100-: 8.24321600

**Periodic interest rate**is the rate of interest earned over a single compounding period. For example, a bank may state that a particular CD pays a periodic quarterly interest rate of 3% that compounds 4 times a year.**Stated annual interest rate**, also called**quoted interest rate**, is the annual rate of interest that does not account for compounding within the year. It is the annual interest rate quoted by financial institutions and equal to the periodic interest rate multiplied by the number of compounding periods per year. For example, the stated annual interest rate of the above CD is 3% x 4 = 12%. It is strictly a quoting convention, and it does not give a future value directly.**Effective annual rate (EAR)**is the annual rate of interest that takes full account of compounding within the year. The periodic interest rate is the stated annual interest rate divided by m, where m is the number of compounding periods in one year: EAR = (1 + periodic interest rate)^{m}- 1. Note that the higher the compounding frequency, the higher the EAC.^{2}- 1 = 8.16. The annual interest rate is 8%, and the effective annual rate is 8.16%.

*Example*If the nominal interest rate is 8%, find the effective annual rate with quarterly compounding.

**Method 1: By Formula**m = 4, EAR = (1 + 0.08/4)

^{4}- 1 = 0.0824The effective interest rate with quarterly compounding is 8.24%.

**Method 2: Texas Instruments**You will use the Interest Conversion (ICONV) worksheet

1. Press 2nd ICONV to select the worksheet

2. NOM will be displayed with the previous value

3. Press 2nd [CLR WORK] to clear the worksheet

Proceed as shown below:

Keystrokes: Display

2nd ICONV: NOM = previous value

2nd CLRWORK: NOM = 0.00

8 ENTER: NOM = 8.00

DownArrow: EFF = 0.00

DownArrow: C/Y = previous value

4 ENTER: C/Y = 4.00

DownArrow: EFF = 0.00

CPT: EFF = 8.24

**Method 3: HP 12C**After you have set the calculator to END of period and cleared the financial registers, key in the nominal interest rate as a percentage.

Proceed as shown below:

Keystrokes: Display

g END: Previous value

f CLEAR FIN: 0.00000000

f CLEAR REG: 0.00000000

8 ENTER: 8.00000000

4n i 0.66666667

100 CHS PV: -100.00000000

FV: 108.2432160

100-: 8.24321600

We can also calculate the periodic interest rate given the effective annual interest rate.

**Learning Outcome Statements**

CFA® 2021 Level I Curriculum, 2021, Volume 1, Reading 6

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**User Contributed Comments**
26

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

lazyluc |
wrong formula? shouldn't it be rather (1+ periodic interest rate/m)^m ? |

fuller |
the periodic interest rate = stated annual interest rate/m, as stated in the notes. So the formula is correct. i think what you meant was (1 + stated annual interest rate/m)^m |

rickless3 |
the nominal interest rate is the annual interest rate. This rate may be paid out m times during that time, i.e. quarterly is m=4, monthly is m=12, etc. SO the annual percentage yield for a CD where the interest rate of 3.0% is compounded quarterly is calculated by APY = (1 + 0.03/4)^4 - 1 =(approx.) .03033 or 3.033% |

10klub |
Im using the BA II plus and i cant get that answer for anything. |

10klub |
i got it |

Rotigga |
The Correct Way for HP-12C 8 [ENTER] : 8.0000 4 [Divide] i : 2.0000 4 [n] : 4.0000 100 [CHS] [PV] : -100.0000 [FV] : 108.2432 100 [-] : 8.2432 |

adenisov |
what is CD from the first point? |

lexi |
Similar to a fixed deposit |

Khadria |
Periodic Interest Rate = 4% compunding quarterly Stated Annual rate = 4% x 3 = 12% EAR = [(1+.03)^4]-1 = 12.550881% |

Khadria |
! ! ! Sorry its 3% in the above example ! ! ! |

Sana07 |
I cannot get this calculation to work on the HP 12C Platinum calculator and I have used both the example as well as Rotigga's method but I get 16.99 and this I know is incorrect. Can somebody please tell me what the exact keystrokes on the HP 12C Platinum should be?? Thanks, in advance! |

mirfanrana |
for BA II plus 2nd ICONV 15 ENTER down arrow key twice 4 ENTER up arrow key once and press CPT |

challenger24 |
HP 12c platinum n = 2 FV = ? i = 4 FV equals 1.0816 - 1 PV = -1 FV = 0.0816 * 100 PMT = 0 FV = 8.16% |

Bududeen |
to sana07 & Challenger24 hp 12c n=4 i=8/4=2 pv=100chs fv=?=108.2432 EAR=FV-PV hope this help |

raymondg |
could somebody please explain for the BAII I cannot get the answer |

uhupong |
raymondg, just look at second method. |

peteypete |
if you have an education, you don't need to use the special functions on the calculator. |

cleopatraliao |
My BAII cant get it either...its weird... i followed the exact procedure as the instruction booklet... |

callixtus |
Find EAR if annual nominal rate of 7% is compounded daily. HP12C Platinum g END f CLEAR FIN 7 [ENTER] (nominal rate) 365 [n] [divide] [i] (daily rate) CHS PMT FV |

callixtus |
EAR = 7.25% |

nwarrior |
With the BAII Plus you need to push enter after entering the values, hope this helps. |

Chl4072 |
What is EAC? |

sinmani |
BAII Plus - If you press 2nd ICONV you will see below; 1. EFF 2. C/Y 3. NOM You have to provide 2 values i.e. C/Y = 4 and NOM = 8 for 3rd value press cpt and you will get the answer. |

dbedford |
*** very important r/m = discount rate .... you’ll need this for questions in next couple of readings |

dbedford |
And r/m = periodic rate |

kseeba17 |
This calculator is unbearable, such a waste of time. What good reason is there to not be able to see fractions and brackets... |

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