Question:

How can I use mortgage payment schedules to compare an ARM with a fixed rate mortgage?

Mortgage payment schedules can be used for equating ARMs to fixed rate mortgages and finding the maximum beneficial interest rate on an ARM. We will show you how to compare an ARM with a fixed rate mortgage with the help of an example.

Consider a mortgage of \$100,000 to be paid in 15 years. There are two financing options:

• 7% fixed rate
• 5% adjustable rate, re-adjustment after 1st year and then every 2 years

Step 1:

To compare an ARM with a fixed rate mortgage you need to first create a fixed rate mortgage payment schedule and an ARM payment schedule for the periods for which the interest rate is known.

ARM
Month Principal Monthly Payment Interest Payment Amortization
0 \$100,000 \$0 \$0 \$0
1 \$99,626 \$791 \$417 \$374
2 \$99,250 \$791 \$415 \$376
3 \$98,872 \$791 \$414 \$377
4 \$98,493 \$791 \$412 \$379
5 \$98,113 \$791 \$410 \$381
6 \$97,730 \$791 \$409 \$382
7 \$97,347 \$791 \$407 \$384
8 \$96,961 \$791 \$406 \$385
9 \$96,574 \$791 \$404 \$387
10 \$96,186 \$791 \$402 \$389
11 \$95,795 \$791 \$401 \$390
12 \$95,404 \$791 \$399 \$392
Fixed Rate
Month Principal Monthly Payment Interest Payment Amortization
0 \$100,000 \$0 \$0 \$0
1 \$99,684 \$899 \$583 \$316
2 \$99,367 \$899 \$581 \$318
3 \$99,047 \$899 \$580 \$319
4 \$98,726 \$899 \$578 \$321
5 \$98,403 \$899 \$576 \$323
6 \$98,078 \$899 \$574 \$325
7 \$97,751 \$899 \$572 \$327
8 \$97,423 \$899 \$570 \$329
9 \$97,092 \$899 \$568 \$331
10 \$96,759 \$899 \$566 \$333
11 \$96,425 \$899 \$564 \$335
12 \$96,088 \$899 \$562 \$337

Step 2:

Now, you need to find the difference between the monthly payments of the two loans, for the years before the adjustment period starts. This is a monthly figure of \$899-\$791 = \$108. We convert this into a future value to the end of the twelfth month and get FV = \$1,326

Step 3:

To find a benchmark interest rate we need to calculate the rate at which the two loans become equal. If the two loans cost the same, then the monthly payments would be same for the two loans after the adjustment period. Now we can calculate the interest rate.

As some money was saved on the ARM in the 1st year, we subtract that from the remaining ARM balance, so that the two loans cost equal, and calculate the rate on the remaining balance i.e. \$95,404 - \$1,326 = \$94,078

Step 4:

The rate comes out to be 7.36%. This means that if the rate is increased from 5% to 7.36% on the ARM for the rest of its lifetime, the two loans would cost the same.

So if you have a good chance of getting a lifetime rate below 7.36% after the adjustment period, then you should go for the ARM, otherwise go for the fixed rate loan.

*The formulas used in MS Excel were:
=PMT() - for monthly payment
=FV() - for future value
=rate() - for interest rate

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