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# HP 10bii Calculator - Interest Rate Conversions

## Calculator symbol key

The procedures in this document use the following text to represent symbol keys:
 Key Description Text Representation colored key; shift key SHIFT

## Interest rate conversion basics

The Interest Rate conversion application uses three keys:
• SHIFT, NOM%
• SHIFT, EFF%
• SHIFT, P/YR
They convert between nominal and annual effective interest rates.
If the annual nominal interest rate is known, the corresponding annual effective rate can be solved:
1. Enter the nominal rate and press SHIFT, then NOM%.
2. Enter the number of compounding periods and press SHIFT, then P/YR.
3. Calculate the effective rate by pressing SHIFT, then EFF%.
To calculate a nominal rate from a known effective rate:
1. Enter the effective rate and press SHIFT, then EFF%.
2. Enter the number of compounding periods and press SHIFT, then P/YR.
3. Calculate the nominal rate by pressing SHIFT, then NOM %.
In the TVM application, SHIFT, NOM%, and I/YR share the same register.
Interest conversions are primarily used for two types of problems:
• Comparing investments with different compounding periods.
• Solving TVM problems where the payment period and the interest period differ.

## Example of comparing investments

Which of the following three banks has the most favorable interest rate?
First Bank: 6.70 percent annual interest, compounded quarterly.
Second bank: 6.65 percent annual interest, compounded monthly.
Third bank: 6.63 percent annual interest, compounded 360 times per year.

### First bank

 Keys Display Description Press 6, [.], 7, SHIFT, then NOM% 6.70 Stores nominal rate Press 4, SHIFT, then P/YR 4.00 Stores quarterly compounding periods Press SHIFT, then EFF% 6.87 Calculates annual effective rate

### Second bank

 Keys Display Description Press 6, [.], 65, SHIFT, then NOM% 6.65 Stores nominal rate Press 12, SHIFT, then P/YR 12.00 Stores monthly compounding periods Press SHIFT, then EFF% 6.86 Calculates annual effective rate

### Third bank

 Keys Display Description Press 6, [.], 63, SHIFT,then NOM% 6.63 Stores nominal rate Press 360, SHIFT, then P/YR 360.00 Stores compounding periods Press SHIFT, then EFF% 6.85 Calculates annual effective rate
The first bank offers a slightly better rate since 6.87 is greater than 6.86 and 6.85.

## Compounding and payment periods differ

The TVM application assumes that the compounding periods, and the payment periods are the same. Some loan installments or savings deposits and withdrawals do not coincide with the bank's compounding periods. If the payment period differs from the compounding period, adjust the interest rate to match the payment period before solving the problem.
To adjust an interest rate when the compounding period differs from the payment period, complete the following steps:
1. Enter the nominal rate and press SHIFT, then NOM%. Enter the number of compounding periods in a year and press SHIFT, then P/YR. Solve for the effective rate by pressing SHIFT, then EFF%.
2. Enter the number of payment periods in a year and press SHIFT+P/YR. Solve for the adjusted nominal rate by pressing SHIFT, then NOM%.

## Example of calculating monthly payments and daily compounding

Starting today, monthly deposits of \$25 are made to an account paying 5 percent interest, compounding daily (using a 365 day year). What will the balance be in seven years?

### Step 1

Calculate the equivalent rate with monthly compounding.
 Keys Display Description Press 5, SHIFT,then NOM% 5.00 Stores nominal percentage rate Press 365, SHIFT,then P/YR 365.00 Stores bank's compounding periods per year Press SHIFT, then EFF% 5.13 Calculates annual effective rate Press 12, SHIFT,then P/YR 12.00 Stores monthly periods Press SHIFT, then NOM% 5.01 Calculates equivalent nominal percentage rate for monthly compounding
Since NOM% and I/YR share the same register, this value is ready for use in the rest of the problem.

### Step 2

Calculate the future value.
Set to BEGIN mode. Press SHIFT, then BEG/END if annunciator is not displayed.
 Keys Display Description Press 0, then PV 0.00 Stores present value Press 25, [+/-], then PMT -25.00 Stores payment Press 7, then SHIFT, then xP/YR 84.00 Stores total number of payments Press FV 2,519.61 Calculates balance after 7 years

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