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HP 12c Financial Calculator  Mortgages with Balloon Payments
The HP 12c TVM
A set of mathematical tools are built into the HP 12c for evaluating the time value of money (TVM), and the concepts of
the present value of money (PV), the future value of money (FV), periodic payments (PMT), interest rates (i), and the
number of periods (n). There are many standard situations where TVM calculations can be used to solve problems, such
as calculating loan and mortgage variables. The standard HP 12c features allow these problems to be solved easily.
Cash flow diagrams and sign conventions
The sign conventions for cash flows in the HP 12c follow this 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 solve most TVMrelated problems. The
cash flow diagram below represents the borrower viewpoint of the most common mortgage problems with balloon
payment and their relation to the TVM variables.
Figure : Cash flow diagram
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 balloon payment
Example 1
A home priced at $114,400, is bought with a mortgage with a $900 monthly payment for the next 30 years.
The bank quoted an interest rate of 8.75%. If after five years the house must be sold, what is the amount
still owed on the house? The cash flow diagram in Figure 2 illustrates this example.
Figure : Displaying the values in the cash flow diagram
Solution
Enter the relevant values in any order and compute the FV:
Keystroke

Display


Figure : Calculating the balloon payment

Answer
After five years, a balloon payment of $109,467.03 must be made to bank.
Example 2
A $150,000 house is bought with a 20year mortgage loan having an annual interest rate of 6.75%,
compounded monthly. After eight years the family needs to move to another state and the house must be
sold. If they were to pay off the remaining balance on the loan, how much would the final balloon payment
be?
Solution
The regular payment for the 20year original mortgage plan must be calculated first:
Keystroke

Display


Figure : Calculating the monthly payment

This is the monthly payment. Now the new period is established prior to calculate the balloon payment:
Keystroke

Display


Figure : Calculating the final balloon payment

Answer
The final amount owed on the loan, which is a balloon payment, is $133,620.41.
Example 3
The family from previous example was informed (in time) that they would not need to move for two more
years. What would the balloon payment be at that time with this unexpected change?
Solution
Assuming that all previous data is kept in the calculator, it is enough to set the new period and calculate the
balloon payment again:
Keystroke

Display


Figure : Calculating the
balloon payment

Answer
The balloon payment will then be $127,951.50 after ten years.
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