# The Financial Registers

In addition to the data storage registers discussed, the HP-12C has five special registers in which numbers are stored for financial calculations. These registers are designated n, i, PV, PMT, and FV. The first five keys on the top row of the calculator are used to store a number from the display into the corresponding register, to calculate the corresponding financial value and store the result into the corresponding register, or to display the number stored in the corresponding register.

Storing Numbers Into the Financial Registers

To store a number into a financial register, key the number into the display, then press the corresponding key (n, i, PV, PMT, or FV).

Displaying Numbers in the Financial Registers

To display a number stored in a financial register, press RCL followed by the corresponding key.

Clearing the Financial Registers

Every financial function uses numbers stored in several of the financial registers. Before beginning a new financial calculation, it is good practice to clear all of the financial registers by pressing f CLEAR FIN. Frequently, however, you may want to repeat a calculation after changing a number in only one of the financial registers. To do so, do not press f CLEAR FIN; instead, simply store the new number in the register. The numbers in the other financial registers remain unchanged.

The financial registers are also cleared when you press f CLEAR REG and when Continuous Memory is reset. As described in Error Conditions.

The Cash Flow Sign Convention

When entering the PV, PMT, and FV cash flows, the quantities must be keyed into the calculator with proper sign, + (plus) or - (minus), in accordance with …

The Cash Flow Sign Convention: Money received is entered or displayed as a positive value. Money paid out is entered or displayed as a negative value.

The Payment Mode

One more bit of information must be specified before you can solve a problem involving periodic payments. Such payments can be made either at the beginning of a compounding period (payments in advance, or annuities due) or at the end of the period (payments in arrears, or ordinary annuities). Calculations involving payments in advance yield different results than calculations involving payments in arrears. Regardless of whether payments are made in advance or in arrears, the number of payments must be the same as the number of compounding periods.

To specify the payment mode: press g BEG if payments are made at the beginning of the compounding period, press g END if payments are made at the end of the compounding period.

The BEGIN status indicator is lit when the payment mode is set to Begin. If BEGIN is not lit, the payment mode is set to End.

Compound Interest Calculations

Specifying the Number of Compounding Periods and the Periodic Interest Rate

Interest rates are usually quoted at the annual rate (also called the nominal rate): that is, the interest rate per year. However, in compound interest problems, the interest rate entered into i must always be expressed in terms of the basic compounding period, which may be years, months, days, or any other time unit. For example, if a problem involves 6% annual interest compounded quarterly for 5 years, n–the number of quarters–would be 5 x 4 = 20 and i–the interest rate per quarter–would be 6% / 4 = 1.5%. If the interest were instead compounded monthly, n would be 5 x 12 = 60 and i would be 6% / 12 = 0.5%.

Calculating the Number of Payments or Compounding Periods

Press f CLEAR FIN to clear the financial registers. Enter the periodic interest rate, using i or 12/. Enter at least two of the following values: present value, using PV, payment amount, using PMT, future value, using FV. If a PMT was entered, press g BEG or g END to set the payment mode. Press n to calculate the number of payments or periods.

If the answer calculated is not an integer, the calculator rounds the answer up to the next higher integer before storing it in the n register and displaying it. For example, if n were calculated as 318.15, 319 would be the displayed answer. The value of n is rounded up by the calculator to show the total number of payments needed: n-1 equal, full payments, and one final, smaller payment.

Calculating the Periodic and Annual Interest Rates

Press f CLEAR FIN to clear the financial registers. Enter the number of payments or periods, using n or 12x. Enter at least two of the following values: present value, using PV, payment amount, using PMT, future value, using FV. If a PMT was entered, press g BEG or g END to set the payment mode. Press i to calculate the periodic interest rate. To calculate the annual interest, key in the number of periods per year, then press x.

Calculating the Present Value

Press f CLEAR FIN to clear the financial registers. Enter the number of payments or periods, using n or 12x. Enter the periodic interest rate, using i or 12/. Enter either or both of the following: payment amount, using PMT, future value, using FV. If a PMT was entered, press g BEG or g END to set the payment mode. Press PV to calculate the present value.

Calculating the Payment Amount

Press f CLEAR FIN to clear the financial registers. Enter the number of payments or periods, using n or 12x. Enter the periodic interest rate, using i or 12/. Enter either or both of the following: present value, using PV, future value, using FV. Press g BEG or g END to set the payment mode. Press PMT to calculate the payment amount.

Calculating the Future Value

Press f CLEAR FIN to clear the financial registers. Enter the number of payments or periods, using n or 12x. Enter the periodic interest rate, using i or 12/. Enter either or both of the following: present value, using PV, payment amount, using PMT. If a PMT was entered, press g BEG or g END to set the payment mode. Press FV to calculate the future value.

Odd-Period Calculations

The examples presented so far have dealt with financial transactions in which interest begins to accrue at the beginning of the first regular payment period. However, interest often begins to accrue prior to the beginning of the first regular payment period. The period from the date interest begins accruing to the date of the first payment, begin not equal to the regular payment periods is sometimes referred to as an ‘odd first period.’ For simplicity, in using the HP-12C we will always regard the first period as equal to the remaining periods, and we will refer to the period between the date interest begins accruing and the beginning of the first payment period as simply the ‘odd period’ or the ‘odd days’. (Note that the odd period is always assumed by the calculator to occur before the first full payment period.) You can calculate i, PV, PMT, and FV

for transactions involving an odd period simply by entering a noninteger n. This places the calculator in Odd-Period mode. The integer portion of n specifies the number of full payments periods, and the fractional part specifies the length of the odd period as a fraction of a full period.

At your option, the calculations of i, PV, PMT, and FV can be performed with either simple interest or compound interest accruing during the odd period. If the C status indicator in the display is not lit, simple interest is used. To toggle compound interest mode–turn the C indicator on or off–press STO EEX.