Quantitative Methods: Basic Concepts

Reading 6. The Time Value of Money

Learning Outcome Statements

c. calculate and interpret the effective annual rate, given the stated annual interest rate and the frequency of compounding;

CFA Curriculum, 2020, Volume 1

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Subject 2. Calculate the Effective Annual Rate

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

  • 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.

    For example, a $1 investment earning 8% compounded semi-annually actually earns 8.16%: (1 + 0.08/2)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 = 0.0824
The 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.

Take a QuizThere are 6 basic questions available.

User Contributed Comments 26

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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...