Saturday, February 17, 2024

TI-30Xa Algorithms: Annuity Factors

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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