This document explains the procedures used to convert between nominal, and annual effective interest rates.

Converting a Nominal Rate to an Effective Rate

Given a nominal interest rate and the number of compounding periods per year, this procedure computes the effective annual interest rate:

1. Press g, then END and f CLEAR FIN
2. Key in the annual nominal rate as a percentage, then press ENTER
3. Key in the number of compounding periods per year, then press n, [÷], then i
4. Key in 100 then press CHS, ENTER, and then PV
5. Press FV, then [+] to obtain the effective annual interest rate

Examples of converting a Nominal Rate to an Effective Rate

Following are examples of converting nominal rates to effective rates compounded quarterly, monthly, and daily.

Example 1

What is the effective annual interest rate if the annual nominal rate of 5 ¼ % is compounded quarterly?

Keystrokes	Display	Explanation
Press g, then END		Set to end mode
Press f, then CLEAR FIN		Clear the financial registers
Type in 5.25, then press ENTER	5.25	Nominal rate
Press 4, n, [÷],then i	1.31	Quarterly interest rate.
Type 100, then press CHS, then ENTER
Press PV, FV, then [+]	5.35	Percentage effective rate.

Example 2

What is the effective annual interest rate if the annual nominal rate of 7% is compounded monthly?

Keystrokes	Display	Explanation
Press g, then END		Set to end mode
Press f, then CLEAR FIN		Clear the financial registers
Press 7, then ENTER	7.00	Nominal rate
Press 12, n, [÷], then i	0.58	Monthly interest rate.
Press 100, CHS, then ENTER
Press PV, FV, then [+]	7.23	Percentage effective rate.

Example 3

What is the effective annual interest rate if the annual nominal rate of 7% is compounded daily?

Keystrokes	Display	Explanation
Press g, then END		Set to end mode
Press f, then CLEAR FIN		Clear the financial registers
Press 7, then ENTER	7.00	Nominal rate
Press 365, n, [÷], then i	0.02	Daily interest rate.
Press 100, CHS, then ENTER
Press PV, FV, then [+]	7.25	Percentage effective rate.

Converting an Effective Rate to a Nominal Rate

Given an effective interest rate and the number of compounding periods per year, this routine calculates the nominal interest rate.

1. Press f, then CLEAR FIN
2. Key in the number of periods per year, then press n
3. Key in 100, press ENTER, then PV
4. Key in the effective annual rate as a percentage, then press [+], CHS, FV, then i
5. Press RCL, n, then [×] to obtain the annual nominal rate

Example of converting an Effective Rate to a Nominal Rate

Find the nominal rate if the effective rate is 5.35% compounded quarterly.

Keystrokes	Display	Explanation
Press f, then CLEAR FIN		Clear the financial registers
Type 4, press n, then 100
Press ENTER, then PV	100.00
Type 5.35, press [+], then CHS	-105.35
Press FV, then i	1.31	Percent quarterly interest rate
Press RCL, n, then [×]	5.25	Percent nominal interest rate

Converting a Nominal Rate to a continuous Effective Rate

This procedure converts a nominal annual interest rate to the continuous effective rate.

1. Press 1, then ENTER
2. Key in the nominal rate as a percentage then press [%]
3. Press g, e^x, then Δ%

Example of converting a Nominal Rate to a Continuous Effective Rate

What is the effective rate resulting from a 5 ¼% passbook rate with continuous compounding?

Keystrokes	Display	Explanation
Type 1, then press ENTER	1.00
Type 5.25, then press %	0.05
Press g, then ex	1.05
Press [Δ%]	5.39	Continuous rate