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 | Set to end mode | |

Press | Clear the financial registers | |

Type in | 5.25 | Nominal rate |

Press | 1.31 | Quarterly interest rate. |

Type | ||

Press | 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 | Set to end mode | |

Press | Clear the financial registers | |

Press | 7.00 | Nominal rate |

Press | 0.58 | Monthly interest rate. |

Press | ||

Press | 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 | Set to end mode | |

Press | Clear the financial registers | |

Press | 7.00 | Nominal rate |

Press | 0.02 | Daily interest rate. |

Press | ||

Press | 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 | Clear the financial registers | |

Type | ||

Press | 100.00 | |

Type | -105.35 | |

Press | 1.31 | Percent quarterly interest rate |

Press | 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**,**e**, then^{x}**�%**

**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 e | 1.05 | |

Press [�%] | 5.39 | Continuous rate |

Updated On: 12.09.20