 
Calculating
Adjustable Rate Mortgage
(ARM) Payments
Adjustable rate mortgages present a little more complicate procedure for
calculating mortgage payments. This complication results from two factors.
First, the interest rate is allowed to adjust periodically (usually annually),
and second, the initial rate is usually set so low that even if interest rates
do not increase, the payments will usually increase for the first three or four
years. When working with an ARM mortgage, the following terms are important:
 The initial rate on the mortgage. This is often referred to as the
teaser rate since it entices people into accepting this type of a loan.
 The index rate is the interest rate indicated by the index the bank
uses. Sometimes this index is the prime rate.
 The profit margin is the amount of interest that is to be added to
the index rate. This profit margin is often listed in basis points. A
basis point is 1/100 of a percent. Thus, if the lender was charging 250
basis points profit, the lender would add 2.5% to the index rate. In the
early years of the loan, this creates a hidden rate. The hidden rate
is the rate the loan will eventually increase to if there is no change in
the index rate. It is the sum of the index rate and the base rate. Whenever
the annual rate charged is less than the hidden rate, the interest rate
charged will increase the following year.
 The annual cap is the maximum amount of increase (or decrease) in
the interest rate from the previous year's rate. For example, if last year's
interest rate was 10% and the annual cap was 1.5%, the maximum interest rate
that could be charged is 11.5%.
 The lifetime cap is the maximum amount of increase (or decrease) in
the interest rate from the initial rate on the mortgage.
Let's try it with a problem
Suppose you wish to find the initial monthly payment necessary to amortize a
$100,000 mortgage for 30 years at 6.5% nominal interest. Suppose that this loan
is an ARM loan and that the 6.5% is the teaser rate, the current index is 5.5%,
the profit margin is 325 basis points (3.25%), the annual cap is 1.5%, and the
lifetime cap is 6%. Assuming that the index rate did not change during the
loan's 30 year term, what would the payment be for years one through three?
Now let's compute the problem
 First, you calculate the initial mortgage payment just as any other loan.
 Enter the proper payments per 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 12,
then push
the orange SHIFT key
, then
the P/YR key.
We use 12 since the loan requires monthly payments.
 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 30,
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 6.5 and then
pressing the I/YR
key. An interest rate of 6.5 was used since it was the initial (teaser)
rate.
 Next,enter the amount of the loan (what the bank gives you)
key.
In our problem, we enter the Present Value by pressing
100000, then the PV
key.
 Finally all that is necessary is push the PMT
key.
In our problem, we press the PMT
key to compute the monthly payment.
The display then shows 632.07 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 $100,000 today, we must pay $632.07
each month for the next thirty years.)
 Since the hidden rate of 8.75% (5.5% + 3.25%) is greater than the 6.5% that
was charged the first year, the interest rate will increase the next year, that
payment would be calculated as follows:
 The first step is to calculate the balance on the mortgage after the
previous year's payments. (This assumes that the interest rate will
adjust annually. If it adjusts more or less frequently than that, simply
calculate the balance after the last payment.) This is accomplished by
entering the number of years that remain on the mortgage, hitting
the orange SHIFT key
key,
then xP/YR key, and then the PV
key.
In our problem, we enter the number of years that remain on the
mortgage, 29 in this case, then push
the orange SHIFT key
key,
the xP/YR key, and then the PV
key. The display shows 98,882.27.
 Next, enter the new interest rate per year and then press the I/YR
key.
In our problem,
enter the new interest rate per year, 8 (6.5% + the annual cap of
1.5%), and then press the I/YR
key.
 Finally, all that is necessary is push the PMT
key. This is the payment for the second year. If the hidden rate is still
higher than the current rate, then these three steps will be repeated.
In our problem,
all that is necessary is push the PMT
key. The display shows 731.68, the payment for the second year.
Since the
hidden rate, 8.75% is still higher than the current rate, these three steps
will be repeated to compute the payment for the third year.
Now, the first step is to calculate the balance on the mortgage
after the previous year's payments. This is accomplished by entering the
number of years that remain on the mortgage, now 28 years, hitting
the orange SHIFT key
key,
the xP/YR key, and then the PV
key. The display shows 97,980.15.
Next, enter the new interest rate per year, 8.75, and then press the I/YR
key. (Since 8% + the annual cap of 1.5% exceeds the hidden rate, only the
hidden rate is used. Without any changes in the index rate, the loan
interest rate will remain at 8.75% for the remaining term.)
Finally, all that is necessary is push the PMT
key. The display shows 782.57, the payment for the third year (and
remaining years if the index rate does not change).
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Copyright © 2005 Dr. Jerry D. Belloit
