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HP 17BII and HP 17BII+: Finance Solver Equations

HP 17BII and HP 17BII+:  Sales Tax, Substantial Presence Test, Automobile Purchase, Principal Interest Property Tax & Insurance (PITI), Retirement Accounts

Note:  Some equations have the L (Let) and G (Get) functions, which are not available on the brown keyboard of the 17BII+ (around 2003). 

Sales Tax:  Determine the total amount of taxable items and non-taxable items.

AMT=NTAX+TXBL*(1+R%÷100)

AMT:  Total Amount
NTAX:  Items not subject to sales tax
TXBL:  Items subject to sales tax
R%:  sales tax rate

Example 1:  A company purchases equipment which costs $99.99, which was subject to 9.5% sales tax, which includes $139.99 of services.  The services are not subject to sales tax.  What is the total invoice? 

Input:
NTAX:  139.99
TXBL: 99.99
R%:  9.5(%)

Output:
AMT = 249.48

The total of the invoice is $249.48.

Example 2:  During an audit, a company finds an invoice with the total of $236.40 (amount), and the invoice listed non-taxable services of $146.50.  The company lives in a county where the sales tax is 8.75%.  What is the amount of taxable items? 

Input:
NTAX:  146.50
R%:  8.75(%)
AMT:  236.40

Output:
TXBL = 82.67

The amount of taxable items on the invoice is $82.67.

Substantial Presence Test

For more information about the substantial presence test, please click here:  http://edspi31415.blogspot.com/search?q=substantial+presence+

This equation uses Let and Get. 

SPT=IF(L(X:DDAYS(D:12.31+FP(100*D)÷100:1)>183:DATE(D:183):DATE(1.01+(FP(100*D)+.0001)÷100:IP(183-G(X)÷3)))

STP:  Number of days calculated for the Substantial Presence Test
D:  Date (in the format DD.MMYYYY)

Example 1:

D:  1.052019 (1/5/2019),  SPT = 7.072019 (7/7/2019)

Example 2:

D:  6.182008 (6/18/2008), SPT = 12.182008 (12/18/2008)

Example 3:

D:  9.262018 (9/26/2018), SPT = 6.012019 (6/1/2019)

Example 4:

D:  7.102017 (7/10/2017), SPT = 5.062018 (5/6/2018)

Financing the Purchase of an Automobile

This equation deals with the purchase of an automobile. 

AUTO:PRICE*(1-DISC%*.01)*(1+STAX%*.01)-DOWN=PMT*USPV(I%÷12:YRS*12)

PRICE: Sticker price of the automobile
DISC%:  Discount percent
STAX%: Sales tax rate
DOWN:  Down payment (amount)
PMT:  Payment of the loan
I%:  Interest rate of the loan
YRS: Number of years of the loan

Example 1:  The sticker price of a car is $28,000.00.  A discount of 15% is offered.  The car is subject to 10% sales tax.  The dealer offers a 6-year loan at 4.5%.  With $2,000, what is the monthly payment?

Input: 
PRICE: 28000.00
DISC%: 15
STAX%:  10
DOWN: 2000
I%:  4.5
YRS: 6

Output:
PMT = 383.83

The monthly payment is $383.83. 

Example 2:  Assuming the same facts from Example 1, expect the buyer wants to pay no more than $350.00 a month.  What is the required down payment?

Input: 
PRICE: 28000.00
DISC%: 15
STAX%:  10
I%:  4.5
YRS: 6
PMT: 350.00

Output:
DOWN = 4131.42

The down payment needs to be $4,131.42.

Real Estate:  Principal Interest Property Tax & Insurance (PITI)

Determine the total payment of mortgage when considering property tax and property insurance. 

PITI=MORT÷USPV(I%÷12:YRS*12)+(PROP$+INS$)÷12

PITI:  Payment including principal, interest, property tax, and insurance
MORT:  Mortgage amount, price of the property
I%:  Annual interest rate
YRS: Number of the years of the mortgage
PROP$:  Annual property tax
INS$:  Annual property insurance

Example:  A buyer purchases a home with a price of $200,000.00.  The amount is to be financed.  The loan lasts for 30 years and 5% interest rate.  There is annual property tax of $1,200.00 with insurance of $395.95.  What is the buyer’s PITI?

Input:
MORT: 200000.00
I%:  5
YRS: 30
PROP$:  1200.00
INS$:  395.95

Output:
PITI = 1206.64

The buyer’s PITI is $1,206.64. 

Retirement Accounts:  Future Value and Earned Untaxed Dividends

Determine the future value and untaxed dividends of tax-free retirement accounts (IRS/Keogh).

There are two versions, the second uses Let (L) and Get (G) functions.

Version 1:
IRA: VAL*0+DIV*0+IF(S(VAL):USFV(I%:YRS)*PMT*(1+I%÷100)-VAL:0)+IF(S(DIV):(USFV(I%:YRS)*(1+I%÷100)-YRS)*PMT-DIV:0)

Version 2:
IRA:(VAL+DIV+L(X:USFV(i%:YRS)*(1+I%÷100)))*0+IF(S(VAL):G(X)*PMT-VAL:(G(X)-YRS)*PMT-DIV)

Input Variables:
I%:  Annual Interest Rate
YRS:  Number of Years
PMT:  Annual Payment

Output Variables:
VAL:  Tax Free Value of the Retirement Account
DIV:  Total Untaxed Dividends Earned

Remember, these are untaxed amounts.

Example:
I%:  6.88
PMT:  1000.00
YRS: 40

Output (Results):
VAL = 206811.01
DIV = 166881.01

Source:
Tony Hutchins, Luiz Vieria, and Gene Wright “HP 12C Platinum Solutions Handbook”  Hewlett Packard.  Revised 03.04  2004

Eddie

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