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## HP 50g Graphing Calculator - House Payment Qualification

The FINANCE menu

The Finance solver is accessed from the WHITE shifted function of the key by pressing . When pressed, a data
entry form is displayed that is used to solve a number of financial math problems.

**Figure : Displays data entry form**

To solve problems using this display, move the cursor using the keys to each field and input its value, if known.
To solve for the unknown value, move the cursor to the field for which you wish to solve, and press the key to register the
choice of , which is displayed above it. The value of the unknown will be calculated and displayed in the field. The solved
value of the variable will be copied to the first level of the command stack in case further calculations with it are desired.

Variables are created whenever a value is stored in one of the financial fields or when it has been solved. These variables (N for
example holds the value for n) can be seen in the menu. When they are no longer needed, they can be deleted just like any
other user-created variables. Values from a previous use of the financial solver remain until the variables holding them are deleted.

Several values are already present on this screen. The number of payments per year is set to 12 for monthly compounding, as
shown to the right of the P/YR: in the screen above. If annual compounding is desired, this value should be changed to 1. If quarterly
compounding is desired, this value should be changed to 4. Just below the P/YR: field, the calculator displays the word END,
signifying that payments are assumed to occur at the end of each period, which would be the case for ordinary annuities. If payments
are desired at the beginning of the period, as would be the case in an annuity due, this value can be changed by moving the cursor
to this field. When the cursor is on this field, is displayed above the key, indicating the calculator will supply a list of
choices (Begin or End) in a small CHOOSE box if this key is pressed. Note that Begin will be displayed as Beg if chosen. To exit from this data entry screen, press the key.

**Figure : Displays the word 'End'**

The HP 50g Financial solver follows the standard convention that money in is considered positive and money out is negative.

House payment qualification

The payment required to pay off a house over time involves the solution of an ordinary annuity with the value of the payment as the
unknown variable. When applying for a house loan or mortgage, the lender takes the applicant’s debt burden into account. A general
guideline applied is that the total debt to income should be below 34% and that the house payment plus taxes and insurance should
be below 27% of total income. If a house payment composed of principal and interest were $900, monthly taxes and insurance might
add an additional $100 a month or more to this payment. This will determine the maximum house payment for which an applicant
may qualify as well as the corresponding maximum loan amount.

Practice solving house payment qualification problems

Example 1

Richard wants to buy a house that costs $170,000 using a 30 year loan at 6% compounded monthly. His annual
income is $55,000. His existing monthly debt includes a car payment of $295 per month and a minimum payment
on his credit card of $25 per month. Property taxes are estimated at $1,300 per year and the annual insurance
premium is estimated at $450 per year. Can Richard qualify for this house loan if the lender applies the 27%/34%
guidelines?

Solution

Assumes RPN mode. Richard’s monthly income is $55,000 divided by 12, or $4,583.33 (if you see a fraction
of 13750/3 in the display, press to convert to a number.)

The maximum house payment (including taxes and insurance) Richard can qualify for is 27% of his monthly
income, or $1,237.50

The required payment on the house is found by the following:

**Figure : Entering the values**

The house payment is $1,019.24 a month. With taxes and insurance, this increases to $1,165.07

**Figure : Displays the values**

with if a fraction is displayed.

**Figure : Displays the values**

The $1,165.07 is the total monthly house payment plus taxes and insurance. Richard’s total monthly debt is
to be less than 34% of his monthly income. The maximum monthly debt Richard can have is 34% of his monthly
income, or $1,558.33

with if a fraction is displayed.

**Figure : Displays the fraction**

Richard’s total debt would be the $1,165.07 house payment, the $295 car payment and the $25 per month
credit card payment. This is a total of $1,485.07, which is less than the maximum monthly debt limit set by the
34% guideline. Note that the key below will swap the order of the two numbers displayed.

**Figure : Displays the values**

Answer

Richard can qualify for this house loan because he meets the 27%/34% guidelines.

Example 2

Caroline wants to buy a house that costs $208,000 using a 15 year loan at 5% compounded monthly. Her annual
income is $75,000. Her existing monthly debt includes a car payment of $365 per month and minimum payments
on her credit card of $96.50 per month. Property taxes are estimated at $1,900 per year and the annual insurance
premium is estimated at $1,150 per year. Can Caroline qualify for this house loan if the lender applies the 27%/34%
guidelines?

Solution

Assumes Algebraic mode. Caroline’s monthly income is $75,000 divided by 12, or $6,250.

The maximum house payment (including taxes and insurance) Caroline can qualify for is 27% of her monthly
income, or $1,687.50

The required payment on the house is found by the following:

**Figure : Entering the values**

The house payment is $1,644.85 a month. With taxes and insurance, this increases to $1,899.02

**Figure : Displays the values**

with if a fraction is displayed.

**Figure : Displays the fraction**

The $1,899.02 is the total monthly house payment plus taxes and insurance. This is larger than the 27%
guideline previously computed.

Answer

Caroline cannot qualify for this house loan because she does not meet the 27% guideline. Perhaps she should
consider a 30 year loan.

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