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# HP Business Calculators - TVM Menu Questions

Introduction
This document addresses TVM Menu questions for the HP 10b, 10bii, 12c, 17bii, and 19bii calculators.
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 Move cursor up cursor-up Move cursor down cursor-down
Determining why the wrong answer appears when using the TVM menu (HP 10b, 12c, 17bii, 19bii calculators)
HP 10b calculator
Before beginning a TVM calculation, be sure to clear the TVM variables: Press SHIFT, CLEAR ALL, set the appropriate payment mode (mortgages and loans are typically END mode calculations; leases are typically BEGIN mode calculations), and specify the number of payments per year (P/YR).
HP 12c calculator
Before beginning a TVM calculation, be sure to clear the TVM variables: Press f, FIN, set the appropriate payment mode (mortgages and loans are typically END mode calculations; leases are typically BEGIN Mode calculations), and enter the periodic interest rate, not the APR.
HP 17bii and 19bii calculators
Before beginning a TVM calculation, be sure to clear the TVM variables: Press SHIFT, CLEAR DATA, set the appropriate payment mode (mortgages and loans are typically END mode calculations, leases are typically BEGIN Mode calculations), and specify the number of payments per year (P/YR).
Determining why the wrong answer or "NO SOLUTION" appears when using the TVM menu (HP 10b calculator)
Be sure to enter a value for four of the five TVM values before solving for the fifth, even if one of the values is zero. (Do not forget to store a zero for FV if the loan is to be completely paid off.) Clearing all the registers (SHIFT, C ALL) before entering known values accomplishes the same thing. Check to see that the calculator is in the appropriate payment mode (BEGIN or END mode) and that P/YR is set correctly.
Determining if the TVM menu functions can be accessed from the Solver (HP 17bii calculator)
TVM menu functions cannot be accessed from the Solver, but the same functions can be performed by copying the appropriate financial formulas into the Solver. A complete list of the functions that can be included in the solver start on page 157 of the HP 17bii Owner's Manual.
Determining if the TVM menu can be used with the Solver (HP 19bii calculator)
The TVM menu cannot be used with the Solver, but the TVM Solver functions can be used to do the same calculations.
The TVM Functions
The five Solver TVM functions allow for equations that do calculations analogous to the calculations done in the TVM menu:
 N ( i%yr : pv : pmt : fv : p/yr : m ) I %yr ( n : pv : pmt : fv : p/yr : m ) pv ( n : i%yr : pmt : fv : p/yr : m ) PMT ( n : i%yr : pv : fv : p/yr : m ) FV ( n : i%yr : pv : pmt : p/yr : m )
Each function calculates one TVM value, given the values for all the others. The parameters of the functions (the contents of the parentheses) are defined identically to the built-in TVM variables described in the following table, except that m stands for BEGIN/END mode. Use m=1 for BEGIN mode and m=0 for END mode. For example, the first function calculates N (the total number of payments or compounding periods), given the annual percentage interest rate, present value, payment amount, future value, number of payments per year, and the BEGIN/END mode.
Give the parameters any legal variable name; for example use LOAN in place of pv. Parameters can also be algebraic expressions. For example, the following equation calculates the monthly payment for a car loan:
CARPMT = PMT (MONTHS : I% YR : PRICE-DOWN : 0 : 12 : 0)
Where MONTHS is the duration of the loan (in months), PRICE is the purchase price, and DOWN is the down payment (pv = PRICE-DOWN, n = months, and the last 0 = END mode). Notice that PMT is not a variable in the equation--it is the name of the function.
The solver TVM variables are not shared with the variables in the TVM menu. For example, the variable I%YR in the CARPMT equation is separate from the TVM variable I%YR.
 Menu Key Description N Stores or calculates the total number of payments (or compounding periods). N can be expressed in any unit of time. For example, years, months, or days. SHIFT, then N Multiplies number in display by P/YR and stores result in N. (If P/YR were 12, then pressing 30, SHIFT, N would store 360 in N). I%YR Stores or calculates the nominal annual interest rate as a percentage. PV Stores or calculates the present value of the series of future cash flows. To a lender or borrower, PV is the amount of the loan; to an investor, PV is the initial investment. PV always occurs at the beginning of the first period. PMT Stores or calculates the amount of each periodic payment. The payments are the same amount and no payments are skipped. Payments can occur at the beginning or end of each period. FV Stores or calculates the future value - the amount of the final cash flow, or the compounded value of the series of previous cash flows. FV always occurs at the end of the last period.
The secondary TVM menu
Press OTHER, cursor-up or cursor-down, then EXIT
 Menu Key Description P/YR Stores the number of payments or compounding periods per year. The value must be an integer in the range of 1 through 999 BEG Sets BEGIN mode; used when payments occur at the beginning of each period END Sets END mode; used when payments occur at the end of each period AMRT Displays the AMRT (amortization) menu for calculating amortization schedules
Determining if the TVM menu uses 360 or 365 days (HP 10b, 12c, 17bii, 19bii calculators)
HP 10b calculator
The Time Value of Money math model compounds interest based on the number of periods per year (P/YR). If set to 12 P/YR, it simply breaks a year into 12 equal periods. If set to 4 P/YR, it breaks the year into 4 equal periods. Some finance institutions say they are compounding monthly but use a different math model, which may give a slightly different answer. The formula used by the HP 10b calculator appears in Figure 1.
Payment Mode Factor: S = 0 for END mode; 1 for BEGIN mode.
Figure : TVM
HP 12c calculator
The Time Value of Money math model uses actuarial amortization. It simply breaks a year into equal periods. Some finance institutions say they are compounding monthly but use a different math model, which may give a slightly different answer. The formula used by the HP 12c calculator appears in the tables and Figures below.
Figure : Percentage
Interest
 n = number of compounding periods i = periodic interest rate, expressed as a decimal PV = present value FV = future value or balance PMT = periodic payment S = payment mode factor (0 or 1) indicating treatment or PMT. 0 corresponds to END, 1 to BEGIN I = interest amount INTG (n) = integer portion of n FRAC (n) = fractional portion of n
Figure : Simple interest
Without an odd period:
Figure : Compound Interest
With simple interest used for an odd period:
Figure : Simple interest for an odd period
With compound interest used for an odd period:
Figure : Compound interest for an odd period
Amortization
 n = number of payment periods to be amortized INTj = amount of PMT applied to interest in period j PRNj = amount of PMT applied to principal in period j PVj = present value (balance) of loan after payment in period j j = period number INT1 = 0 if n = 0 and payment mode is set to BEGIN |PV0xi| RND x (sign of PMT PRN1 = PMT - INT1 PV1 = PV0 + PRN1 INTj = |PVj-1x i| RND x (sign of PMT) for j > 1 PRNj = PMT - INTj PVj = Pvj-1 + PRNj
HP 17bii calculator
The Time Value of Money math model compounds interest based on the number of periods per year (P/YR). If set to 12 P/YR, it simply breaks a year into 12 equal periods. If to 4 P/YR, it breaks the year into 4 equal periods. Some finance institutions say they are compounding monthly but use a different math model, which may give a slightly different answer. The formula used by the HP 17bii calculator is also used by the HP 19bii calculator and appears below in Figure 7.
HP 19bii calculator
The Time Value of Money math model compounds interest based on the number of periods per year P/YR. If set to 12 P/YR, it simply breaks a year into 12 equal periods. If set to 4 P/YR, it breaks the year into 4 equal periods. Some finance institutions say they are compounding monthly but use a different math model, which may give a slightly different answer. The formula used by the HP 19bii calculator appears in Figure 7.
S = PV + payment mode factor (0 for END Mode; 1 for BEGIN mode).
Figure : TVM
Answers are wrong when the AMORT function in BEGIN mode is used (HP 12c calculator)
On the HP 12c calculator, clear the n register (0 n) before using AMORT in BEGIN mode. Then the answers will be correct.

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