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.