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Adjustable Rate Mortgages (ARM)

Adjustable Rate Mortgages are mortgages where the lender adjusts the interest rate each month or at an interval agreed upon by lender and borrower. If rates go down the borrower enjoys the benefits of paying less interest plus paying more off the balance providing the payment remains the same. If rates increase the lender enjoys the benefit of more interest at the expense of the borrower. This type of loan can be be a blessing and a curse. It is a fair gesture by a lender however verifying the balance owing at any time is extremely difficult unless the borrower has the appropriate financial software, such as MORTGAGE2 PRO.

Adjustable rate mortgages (ARM) and variable rate mortgages are different names for the same thing. Americans call them ARMs and Canadians call them variable rate mortgages.

Adjustable rate mortgages can yield tremendous savings to borrowers but the chore of verifying the changing amortization schedule can be overwhelming to a novice who is unfamiliar with amortization schedules. Some lenders will change the rate every month and leave the payment constant. Some lenders will recalculate the payment each month based upon the new rate and this type of ARM is very time consuming. It has been estimated that in North America, Billions of dollars each year in excessive interest is paid to lenders that make errors calculating ARMs. An added problem is, if the errors are at the beginning of the schedule they compound themselves throughout the entire schedule. Unless you verify the calculations you will never know.

The changing rates can be simply typed directly into the amortization SPREADSHEET (yellow column) and the entire schedule is instantly recalculated, as in the example below.

(Screenshot 1)

Using the MORTGAGE2 PRO software, changes in the nominal interest rate (Annual Interest Rate) are typed directly into the SPREADSHEET schedule. Payment #1, 12/14/2000 is the first blended payment and it is based upon the initial 12% as entered in the CALCULATOR. After the first payment was made the rate was changed to 6%. The interest due on a balance of $99,898.91 for the use of the money from 12/14/2000 to 01/14/2001 is $499.49 (.06/12 x 99,898.91).

These large changes were purposely chosen to simplify the example. For example, the interest due on 12/14/2000 is 1% of the $100,000 a nice simple shift of the decimal point. After payment #2 was made the rate was changed to 3% for the upcoming month. The 3% annual interest rate, in the SPREADSHEET, is automatically divided by 12 and multiplied by $99,297.32 for an interest charge of $248.24 on 02/14/2001. The full payment #8, is applied towards reducing the balance to $94,408.52 because the interest rate was changed to zero on line 7 the month before.

 

More Examples

ARM 1

ARM 2

ARM 3

ARM 4


ARM 1

Assume you borrowed $100,000 and amortized the loan for three years starting at 8 % in the first year, 7% in the second year and 6% in the remaining third year. Monthly payments and monthly compounding were selected.

QUESTION: How much interest would you save compared to paying 8% for the entire three years?

Enter the data in the CALCULATOR section of the MORTGAGE2 PRO screen. The amortization schedule for that information will be immediately calculated and shown in the SPREADSHEET amortization schedule, as if the entire loan was to be at 8%. The entire schedule is not going to be at 8%, but you must start out in the calculator as that way then change the interest rates in the SPREADSHEET.

(Screenshot 1)

Once changes are made in the amortization schedule SPREADSHEET the CALCULATOR information is no longer meaningful except as a reference point (Calculator Interest). Changes to the amortization schedule SPREADSHEET are now your focus.

Using your mouse, place the cursor on the 12th payment interest rate cell (yellow) on the amortization schedule and change it to 7.000% and click on the cell, to insure the change is entered. When you click on the cell you will see the amortization schedule spreadsheet cells change indicating a cell change. Hold the shift key down and press the down arrow to highlight the cells down to the 24th payment and the amortization schedule should appear as below;

(Screenshot 2)

Now do a Crtl+V (the standard Windows paste shortcut) and the amortization schedule appears as shown below;

(Screenshot 3)

Do the same thing with interest rate cells 24 to 36 only this time using 6% and the amortization schedule will appear as below;

All changes to the amortization schedule show up as yellow, however, the yellow colour for the portion of the interest rate column at 6%, was changed to green for ease of viewing in this example. Note, the monthly interest $223.83 portion for the 24th payment is determined by the value in the interest rate in the Int% cell above. This is how the program was designed to operate. Thus .07/12 x 38,370.98 = $223.83

(Screenshot 4)

You now have an amortization schedule for three years with a declining rate of 8%, 7% and 6% in the final year. The total interest cost due to the declining rates is $11,804.16 (Spreadsheet Interest) compared to $12,810.92 had you remained at the initial 8% throughout the 36 months (Calculator Interest).

ANSWER: The declining rate, for this 3 year amortized loan, saved you $1,006.76 (12,810.92-11,804.16=1,006.76). The three year amortization period was purposely chosen in order to explain deemed reinvestment and show the significance of the effective interest rate.

A 30 year amortization period example is shown at the bottom of this page and the savings achieved because of the three year declining rate are more significant.

 

THE STORY BEHIND THE STORY

A unique feature of MORTGAGE2 PRO is the ability to generate a negative amortization schedule. By generating an negative amortization schedule (all the payments set to zero) the future value of all the payments at the appropriate interest rates can be calculated. Using the mouse move the cursor up to the first payment and enter 0 (zero) and then click on the cell to ensure the change has been entered. Hold the shift key down and press the down arrow to highlight the cells down to and including the 36th payment line, and then do a Ctrl+V to copy the zero payments all the way down to the 36 th line of the schedule.

(Screenshot 5)

In the balance column at the 36th payment is the value of $123,291.54 This is the future value of $100,000 appreciating at 8% in the first year, 7% in the second year and 6% in the final year. If the lender reinvests each monthly payment when received, this is the true return the lender achieves at the end of three years, that is $23,291.54 on the intial loan of $100,000.

Using an ordinary financial calculator or the MORTGAGE2 PRO utility;

(Screenshot 6)
(Screenshot 7)

The effective interest rate (EIR) of this 3 year loan (ARM) is 7.2287%

As a cross reference, using the free downloadable m2factor.exe utility from the amortization.com site, the interest earned by the lender after 3 x 365 days (deemed reinvestment) is the same, that is $23,291 (see the annual rate below at $23,291.50). When a loan is annually compounded the effective interest rate and the nominal annual interest rate are the same.

(Screenshot 8)

The real time saving convenience of the MORTGAGE2 PRO, negative amortization schedule feature is really appreciated when one needs to evaluate an ARM where the interest rate changes every month, the payments change each month and extra prepayments are made in between regularly scheduled payments. The deemed reinvestment feature would be very very time consuming if done manually as individual present value/future value calculations on a calculator.

As a further point of interest if one used the effective interest rate of 7.2287% with annual compounding and did a negative amortization schedule, the same future value of $123,291.49 is achieved (the yellow highlighted cell in the balance column).

(Screenshot 9)

 

FROM A DIFFERENT PERSPECTIVE

To achieve an effective interest rate of 7.2287% with monthly compounding the stated annual interest rate (aka as the Annual Interest Rate) must be 6.9997%. Comparing the negative amortization (deemed reinvestment) for 36 months for this case must yield the same future value of $123,291.46 (see below within 3 cents).

(Screenshot 10)

Also, to achieve an effective interest rate of 7.2287% with semi-annual compounding the stated annual interest rate (aka as the Annual Interest Rate) must be 7.1026%. Comparing the negative amortization (deemed reinvestment) for 36 months for this case must yield the same future value of $123,291.56 (see below within 7 cents).

(Screenshot 11)

It should now be obvious that the effective interest rate is a very powerful number to know as it describes the return one gets on a loan or mortgage without having to be concerned about the type of compounding the lender uses.

 

Using a 30 year amortization period.

Assume you borrowed $100,000 and amortized the loan for 30 years starting at 8 % in the first year, 7% in the second year and 6% in the remaining third year. Monthly payments and monthly compounding were selected.

QUESTION: How much interest would you save compared to paying 8% for the entire first three years?

The cumulative interest paid if the rate remained at 8% for the first 36 months is $23,695.70 and the cumulative interest paid with the declining rates is $20,601.72 The difference is $3,093.98

ANSWER: You would save approximately $3,094

(Screenshot 12)
(Screenshot 13)

 

ARM 2

Would you have the time to prepare the following ARM schedule shown below where your monthly interest rate was based on prime, plus or minus, an incremental change each month? Can you imagine doing this for a 30 year monthly payment mortgage manually, or trusting your lender to do it correctly? You will also note in this example, a 365 day year was chosen instead of the 360 day "Bankers Year". Each month as the rate changes you simply type in the new rate in the AIR% column (yellow) and the entire schedule is recalculated instantly. You then resave the schedule with the same name or a new name.

(Screenshot 14)

 

ARM 3

The best way to save the most in interest costs using an ARM is to keep the payments the same when the rate goes down and increase the payments when the rate goes up. However most people cannot keep tabs on their mortgage because the lender does not always make the information available on a timely basis. The verification process is always after the fact when your memory is foggy.

Ask your lender if they will follow specific instructions as to keeping the payment constant when the rate declines and increasing the payment when the rate increases, you will be surprised at the answer!!! The MORTGAGE2 PRO software can handle all these scenarios.

 

ARM 4

What if you took out an ARM on July 3rd 2001 as per the conditions in the CALCULATOR below. At the end of the first year would you be able to calculate or would your lender be able to tell you what the effective interest rate (EIR) or the APR was due to the changing interest rate each month?

The EIR of 5.1161898 in the CALCULATOR is only valid if the rate was constant from month to month. To answer the question you change the rate each month to the appropriate values in the SPREADSHEET, then do a negative amortization schedule by changing all the payments to zero and making a note of the balance after one year ($105,571.93) which is really the Future Value that an investor looks at. Inserting that information in the MORTGAGE2 PRO PV/FV window you arrive at an effective interest rate of 5.571930%

(Screenshot 15)

 

 


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