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:
- Press g, then END and f CLEAR FIN
- Key in the annual nominal rate as a percentage, then press ENTER
- Key in the number of compounding periods per year, then press n, [�], then i
- Key in 100 then press CHS, ENTER, and then PV
- 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 � % 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.
- Press f, then CLEAR FIN
- Key in the number of periods per year, then press n
- Key in 100, press ENTER, then PV
- Key in the effective annual rate as a percentage, then press [+], CHS, FV, then i
- 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.
- Press 1, then ENTER
- Key in the nominal rate as a percentage then press [%]
- Press g, ex, then �%
Example of converting a Nominal Rate to a Continuous Effective Rate
What is the effective rate resulting from a 5 �% 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 [�%] | 5.39 | Continuous rate |
Updated On: 12.09.20