TI-30Xa Algorithms: Annuity Factors
Introduction
Even when a calculator isn't (technically) programmable, algorithms can be applied to scientific and financial calculations.
The calculations take numerical arguments that are stored in the TI-30Xa's three memory slots: M1, M2, and M3. Store amounts into the memory registers by the [ STO ] key.
Careful: For the solar versions of the TI-30Xa, do not press the [ON/AC] button as doing so clears the memory registers.
Today's list of routines deals with annuity factors.
SPFV: Future Value of a Single Present Value Factor
SPFV = (1 + i%)^n
FV = PV × SPFV
SPPV: Present Value of a Single Future Value Factor
SPPV = (1 + i%)^(-n)
PV = FV × SPPV
USFV: Future Value of a Payment Stream Factor
USFV = ((1 + i%)^n - 1) ÷ i%
FV = PMT × USFV
USPV: Present Value of a Payment Stream Factor
USPV = (1 - (1 + i%)^(-n)) ÷ i%
PV = PMT × USPV
where:
PV = present value
PMT = payment
FV = future value
n = number of periods
i% = periodic interest rate
For monthly payments per year:
n = number of years × 12
i% = annual interest rate ÷ 12
For quarterly payments per year:
n = number of years × 4
i% = annual interest rate ÷ 4
For the routines, n is stored in memory register 1 and i% is stored in memory register 2.
n [ STO ] 1
i% [ STO ] 2
SPFV: Future Value of a Single Present Value Factor
[ ( ] 1 [ + ] [ RCL ] 2 [ 2nd ] { % } [ ) ] [ y^x ] [ RCL ] 1 [ = ]
SPPV: Present Value of a Single Future Value Factor
[ ( ] 1 [ + ] [ RCL ] 2 [ 2nd ] { % } [ ) ] [ y^x ] [ RCL ] 1 [ ± ] [ = ]
USFV: Future Value of a Payment Stream Factor
[ ( ] [ ( ] 1 [ + ] [ RCL ] 2 [ 2nd ] { % } [ ) ] [ y^x ] [ RCL ] 1 [ - ] 1 [ ) ]
[ ÷ ] [ RCL ] 2 [ 2nd ] { % } [ = ]
USPV: Present Value of a Payment Stream Factor
[ ( ] 1 [ - ] [ ( ] 1 [ + ] [ RCL ] 2 [ 2nd ] { % } [ ) ] [ y^x ] [ RCL ] 1 [ ± ] [ ) ]
[ ÷ ] [ RCL ] 2 [ 2nd ] { % } [ = ]
Example
Let n = 60, i% = 5
60 [ STO ] 1
5 [ STO ] 2
SPFV: 18.67918589
SPPV: 0.053535524
USFV: 353.5837179
USPV: 18.92928953
Eddie
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