This document explains the procedures used to convert between nominal, and annual effective interest rates.
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HP 12c Calculator  Interest Rate Conversions
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 5¼ % is compounded quarterly?
Key (RPN mode)

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?
Key (RPN mode)

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?
Key (RPN mode)

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.
Key (RPN mode)

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, 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?
Key (RPN mode)

Display

Explanation

Type 1, then press ENTER

1.00


Type 5.25, then press %

0.05


Press g, then e^{x}

1.05


Press [Δ%]

5.39

Continuous rate

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