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HP 12c Financial Calculator  Mortgages with Loan Fees (Points)
Mortgages with loan fees (points)
It is not unusual that, in some mortgage loans, there are related fees charged at the moment the loan amount is disbursed. These fees are often taken as percentages ("points") of the loan amount. In essence, these fees are an instant repayment of part of the loan. However, the periodic payment is computed on the loan amount before these fees are repaid. This has the effect of raising the effective interest rate being paid on the loan. For example, a $100,000 loan with 2 points would have the payment calculated on the $100,000 amount even though 2 points (2% or $2,000 in this instance) would be repaid immediately. The payment would be made as if $100,000 were owed when in fact only $98,000 is owed on the loan.
The HP 12c TVM
A set of mathematics tools has been developed with the purpose of evaluating the time value of money (TVM), and the concepts of the present value of money (PV), future value of money (FV), periodic payments (PMT), interest rates (i), and the number of compounding periods (n). There are many standard situations where TVM calculations can be used to solve problems, like calculating loan and mortgage variables. The standard HP 12c has features to solve problems like these with the five TVM keys , , , and .
Cash flow diagrams and sign conventions
The sign conventions for cash flows in the HP 12c follow the simple rule: money received is positive (arrow pointing up), money paid out is negative (arrow pointing down). The key is keeping the same viewpoint through each complete calculation. The regular use of cash flow diagrams allows a faster approach to the solution in most TVMrelated problems. The cash flow diagram below represents the borrower viewpoint of the most common mortgage problems with fees and their relation with the TVM variables.
Figure : Cash flow diagram
Setting up and/or calculating each of these values is a matter of using the HP 12c TVM already existing features. There are also two functions meant to be an aid when entering or retrieving annual values for and : and . Pressing is the same as pressing , meaning the number of years can be keyed in and stored as number of months automatically. Pressing is the same as pressing , meaning the yearly interest rate can be keyed in and stored as monthly interest rate automatically. It is also possible to retrieve the yearlyrelated values by pressing (number of years) and/or (yearly interest rate) whenever necessary.
Practice solving mortgage problems with points
Example 1
A family wants to settle a mortgage to buy a home rated $114,400. The bank offers a 30year mortgage loan with a 2point fee, and with an annual interest rate of 8.75%. What are the actual loan amount and the monthly payment? The cash flow diagram in Figure 2 illustrates this example.
Figure : Values entered in the cash flow diagram
Solution
First, the actual loan amount must be calculated and already set as PV. If the amount disbursed is $114,400, and it has a 2point fee embedded, then the procedure to calculate the actual loan amount is the same one used to calculate price given margin and cost:
Keystroke

Display


Figure : Calculating the actual loan amount

Now it is enough to enter the remaining values in any order and compute the PMT:
Keystroke

Display


Figure : Calculating the monthly payment

Answer
For this 2point fee mortgage, the actual loan amount is $116,734.69 and the monthly payment is $918.35.
Example 2
Having all data from previous example still in the calculator memory, calculate the effective annual percentage rate (APR).
Solution
To calculate the effective APR, the disbursed amount of money ($114,400) is then taken as the PV:
Keystroke

Display


Figure : Calculating the effective annual percentage rate

note:
The interest calculated with is the monthly interest; with the keystroke sequence the annual rate is brought to the display.
Answer
The effective APR is 8.97%.
Example 3
A small commercial building needs improvements and a local bank offers a 25year, $350,000.00 mortgage at 6.85% annual interest with a 2.5point fee. Calculate both the disbursed amount and the monthly payment.
Solution
First the monthly payment is obtained when the actual loan amount is considered as PV:
Keystroke

Display


Figure : Calculating the monthly payment

To calculate the disbursed amount given the actual loan amount, simply subtract 2.5% from it:
Keystroke

Display


Figure : Calculating the amount available for improvements

Answer
The regular monthly payment will be $2,440.34 and the actual amount available for improvements with this mortgage is $341,250.
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