 Article byHarsh Katara An Adjustable-rate mortgage calculator is a type of calculator wherein the user can calculate the periodical installment amount wherein interest rate changes after fixed intervals throughout the life of the borrowing period.

[P x R x (1+R)^N]/[(1+R)^N-1]

Wherein,
• P is the loan amount
• R is the rate of interest per annum
• N is the number of period or frequency wherein loan amount is to be paid
\$
%

The formula for computing Adjustable Rate Mortgage is per below steps:

Mortgage Initial Payment with Fixed-Rate

EMI = (P * R * (1+R)^N)/((1+R)^N-1)

Next, we need to find out the outstanding principal balance just before the rate changes.

Mortgage subsequent payments

EMI = (P * R’ * (1+R’)^N)/((1+R’)^N-1)

Wherein,

• P is the loan amount
• R is the rate of interest per annum
• R’ is the rate applicable subsequently.
• N is the number of periods or frequency wherein the loan amount is to be paid.

This calculator embraces the variable rate mortgage versus an only . These kinds of loans are generally offered by Bank as the bank will not like to lock in a rate for an entire period of the loan, and if they do so, they will face interest rate risk. If in the future, the interest rate goes up, the bank would still be charging less interest rate to its customers and hence will affect their revenue. Further, the cost of operating for the bank could go up, and if they have lent at a fixed rate, then that shall impact their margins and could eventually impact their revenue statement. Further, even customers prefer floating rates as, and when rates fall, they would be benefited by reduced installment amount and reduction in interest outgo. This calculator shall be used to calculate what would be the periodically new installment when there is a change in the rate of interest during the life of the loan.

### How to Use the Adjustable Rate Mortgage Calculator?

One needs to follow the below steps in order to calculate the Mortgage Points benefits.

1. Beginning with the 1st step, one needs to enter the loan amount, which is the principal amount: 2. Multiply the principal by a rate of interest, which is fixed during the initial borrowing. 3. Now, we need to compound the same by rate until the loan period. 4. We now need to discount the above result obtained in step 3 by the following: 5. After entering the above formula in excel, we shall obtain installments periodically.

6. In the initial period, banks would have offered the terms when the rate would change. Calculate the outstanding principal balance just before that rate change.

7. Repeat steps from step 4 but this time with the new interest rate applicable and with an outstanding period.

8. If there is another rate change, then step 6 and step 7 will be repeated until the final rate change is considered.

### Adjustable Rate Mortgage Calculator Example

Mr. Bean has taken a loan for a very short-term mortgage loan that is for 5 years, and the term is 3/1 ARM, and which means that the rate of interest will remain fixed for 3 years and after that rate of interest shall change for the remaining of the term annually. The initial interest rate was 6.75%. It will be reset by 0.10% on every reset date. Based on the given information, you are required to calculate the total mortgage installment amount at each reset date, assuming the initial loan amount was \$100,000, and installments are paid on a monthly basis.

Solution:

We will first calculate the monthly installments based on the initial loan amount as the first step.

The monthly rate of interest will be 6.75% / 12, which is 0.56%, and the period would be 5 years x 12, which is 60 months.

EMI = (P x R x (1+R)^N)/((1+R)^N-1)
• = (\$100,000 x 0.56% x (1 + 0.56%)^60 ) / ( (1 + 0.56%)^60 – 1 )
• = \$1,968.35

Monthly Installments based on the initial loan amount is shown below:

Now the rate of interest changes to 6.75% + 0.10% which is 6.85% at end of 3 years and now the remaining period will be (5 x 12) – (3 x 12) that is 60 – 36 which is 24 months. Now we need to find out the principal balance at the end of year 3 which can be calculated per below:

The monthly rate of interest will be 6.85% / 12 which is 0.57% and the outstanding principal balance is 44,074.69.

At the end of 3 years

New EMI = (P x R’ x (1+R’)^N)/((1+R’)^N-1)
• = (\$44,074.69 x 0.57% x (1 + 0.57%)^24 ) / ( (1 + 0.57%)^24 – 1 )
• = \$1,970.34

Monthly Installments based on the initial loan amount is shown below:

Now again rate will be changed at end of 4th year which shall be 6.85% + 0.10% which is 6.95% and monthly it shall be 6.95% / 12 which is 0.58% and loan period outstanding would be ( 5 x 12 ) – ( 4 x 12 ) which is 60 – 48 which is 12 months. Now we shall find out the principal balance outstanding at end of period 4 per below:

At the end of 4 years

New EMI = (P x R’ x (1+R’)^N)/((1+R’)^N-1)
• = (\$22,789.69 x 0.58% x (1 + 0.58%)^12 ) / ( (1 + 0.58%)^12 – 1 )
• = \$1,971.39

Monthly Installments based on the initial loan amount is shown below:

### Conclusion

An adjustable-rate mortgage or ARM mortgage calculator could be a smart choice for those borrowers who are planning to repay off the borrowing in entire within a specific period or those who shall not be hurt financially when there is an adjustment in interest rate.

This has been a guide to the adjustable-rate mortgage calculator. Here we discuss how to calculate the periodical installment amount using adjustable-rate mortgage along with step by step examples. You may also take a look at the following useful articles –