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Calculating a Mortgage Payment

The basic steps in calculating a mortgage payment are as follows:

  1. Enter the Payments/Year
  2. Enter the rest of the information you know
  3. Solve for the unknown.

Let's try it with a problem
Suppose that you borrow $1,000 for five years and agree to repay the loan in equal, annual installments that will yield the lender 8 percent per year. What would your annual installments would be?

First, let's see what we know

  • We know that you will receive $1,000 today. That indicates that the Present Value (PV) is $1000 since you receive it at the beginning.
     
  • We know that the number of years (xP/YR) is 5.
     
  • We know that the annual interest rate is 8% (8 is the I/YR).
     
  • Finally, we may assume that the periods per year is one since we are not told it is monthly, quarterly, etc. (If the payments per year would have been, for example, monthly, the problem would have read, ". . . yield the lender 8% per year, compounded monthly.")

Now let's compute the problem

  1. Enter the Payments/Year.
    You first must type in the appropriate number (eg. monthly would be 12, quarterly would be 4, etc.), then push the orange SHIFT key , then the P/YR key.

    In our problem, first we must enter the appropriate payments per year by pushing 1, then push the orange SHIFT key , then the P/YR key .
  2.  

  3. Enter the rest of the information you know.
    The order of the next three steps is not important, but I recommend that you follow across the financial tour of your calculator from left to right.
     
    • If you do this, then the next step would be to enter in the proper number of years. You first type the appropriate number, then push the orange SHIFT key , then the xP/YR key.

      In our problem, next we will enter the number of years by pushing 5, then the orange SHIFT key , then the xP/YR key.

       

    • Now, enter the appropriate interest rate per year. This is done by entering the appropriate annual interest rate as a whole number, not as a decimal (the calculator will convert it to decimal automatically), then pressing the I/YR key.

      In our problem, now we will enter the interest rate per year by pushing 8 and then pressing the I/YR key.

       

    • Next, enter the amount of the loan (what the bank gives you) key.

      In our problem, next we enter the Present Value by pressing 1000, then the PV key.
  4.  

  5. Solve for the unknown.
    Finally, all that is necessary is push the PMT key to compute the answer.

    Correct Answer
    The display then shows -250.46 if the display was set to show two decimal places. Note that the answer is negative. This indicates that the direction of the cash flow is out. (This is logical if we will be getting $1000 today, we must pay $250.46 each year for the next five years.)

     

Would you like to review the mathematics of this calculation?

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Copyright 2005  Dr. Jerry D. Belloit