**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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