Refinancing an existing mortgage is a major decision and there are many factors that you take into account, to ensure that you benefit in the long term.

I recently refinanced my mortgage from a 30 year 7/1 ARM to a 30 year fixed rate.

One of the straightforward reasons of refinancing is when you are on a fixed rate and you can refinance to move to a lower fixed rate.

The simple calculation is take the total of closing costs and any points you have to pay, and divide it by the monthly savings in payment. That would give you the time in which you will recoup the closing costs and points.

N = (C + P) / (OP – NP)

N = the number of months for which you must keep the mortgage or the home for the refinance to make sense.

C = total closing costs as provided by the lender’s disclosure statement

P = Points you may additionally pay to lower the rate further. Sometimes this may be included in C already.

OP = Old Payment, NP = New Payment [Use the calculator at bankrate.com]

Easy, right? The above formula also helps in figuring out how many points you should pay to lower your rate. Note that P and NP will vary accordingly.

But there are many people who are on an Adjustable Rate Mortgage (ARM) where either the rate already floats with market or will float after a fixed period.

Typically ARM mortgage rate during the fixed period (7 years for a 7/1 ARM) is lower than a 30 year fixed rate mortgage. But the interest rate risk is completely passed on to you in future.

Hence as the interest rates dip in the market, it may be wise according to one’s situation to refinance to a 30 year fixed.

I vacillated with this decision for a long time as I had a 3.625% 7/1 ARM since last one year. However since then the interest rates started ticking upwards and as the periodic dips came in, I was looking for an opportunity to move to a fixed rate.

But getting a 3.625% or lower fixed rate is not possible today. So I had to refinance to a 4.125% fixed rate. This is counter intuitive to the logic and calculation given above for a fixed->fixed refinance. How does one even justify a slightly higher payment and larger interest component post a refinance?

Here are the factors I considered. This is according to my financial situation and long term goals. Your situation may require to hold the ARM with no problems.

*I want to keep the house for long term. This is the most important factor.**To save the uncertainty of interest rate risks in 7 years, initially my strategy was to pay off the mortgage as much as possible in the first 7 years and then refinance at the prevailing rates for the remaining balance.**To do above, I had to make substantial extra payments towards the mortgage, which skewed my asset allocation (see my earlier post on this: The Paid Piper of Hamelin) more towards Home Equity or Real Estate.**On the other hand, the fixed mortgage (and hence fixed payments) will give me the peace of mind and flexibility to invest more in other assets (instead of throwing extra money to the mortgage).**There is no risk of interest rates (and payments) going higher in the 8th year.*

But how does the math add up? It is not as straightforward as the previous formula.

Lets take the following mortgage and refinance decision.

- Starting balance – $100,000
- Acquired at 7/1 ARM 3.625% ARM (lifetime cap at 8.625%)
- After one year, refinance to 4.125% fixed for 30 years

Lets run the numbers in two scenarios. You can read my post on The Paid Piper of Hamelin to determine which below scenario/strategy will apply to you.

If I keep paying extra I can payoff the mortgage in about 11 years.

You can use the mortgage calculator at bankrate.com to calculate the total interest paid in both cases.

- In the 7/1 ARM, I assumed the 3.625% in the first 7 years during which majority of the principal is paid off. For simplicity, the rate is assumed to be fixed till the mortgage is completely paid off in about 11 years.
- In the fixed rate, the calculation is done with 4.125% on the current balance and assuming same extra payments per month.

Original principal on the 7/1 ARM at 3.625%. – Extra payment of $465/mo, which is same as the monthly payment (thus effectively paying double).

After one year of payoff on the 7/1 ARM, the balance will be $92000 and the interest paid will be $3500. Now lets say the balance is refinanced at 4.125% and the extra prepayment per month is kept steady.

*Since the 7/1 ARM was paid off quite a bit, the cost of remaining balance at 4.125% actually comes pretty close. If you add the interest already paid on the 7/1 ARM, then definitely the fixed rate is costlier ($25000 vs. $21369) simply due to the higher rate and the added refinance costs. However the above 7/1 ARM case also assumes that the rate does not increase at all between 8-12 years. So in reality, the savings of 7/1 ARM may cancel out in favor of the fixed rate, if the rate moves up steadily. *

Now what if I don’t pay extra and invest the rest?

This is tricky calculation but for the 7/1 ARM if I assume the interest rate will touch the maximum (8.625%), then the overall interest paid over 15, 20 and 30 years will be much more (nearly double) than the fixed rate mortgage.

Even with the slightly higher monthly payment, if I invest the extra money according to asset allocation, I should come out better over the long term. Lets run the numbers again.

In case of the fixed rate, the total interest payment in 30 years will be in the range of $72983. Lets add the refinancing costs of $4500 and interest already paid in first year of 7/1 ARM- $3500.

*Note that the balance after maintaining the 7/1 ARM for one year, without paying any extra is $98000.*

Total cost for fixed rate 4.125% = $72,983 + $3500 + $4500 = $80,983

Now assuming the full risk of the ARM (no refinancing), the calculation comes out to be (done in two steps):

- First 7 years, total interest paid = $23,611 and balance = $85000

- For next 23 years, since the spread is 3.625%-8.625%, we take the median 6.125% and calculate the total interest to be paid on the balance $85,302.91 in 23 years.

Total cost for the ARM at 3.625% = $23,611 + $73,669 = $97,280

*Thus the total interest paid for the (3.625%-8.625%) 7/1 ARM will be much higher ($97,280) compared to $80,983 paid on a fixed rate of 4.125%.*

*Exercise: Try the above calculations if the 7/1 ARM is kept for a longer duration (than 1 year) before a refinance to fixed rate. I believe the savings will be more as you are paying down more at lower rate of the 7/1 ARM, but then you are assuming the risk of interest rates as you delay further. *

So there are both behavioral as well as mathematical consideration behind such a refinance decision.

The most obvious behavioral factor is that ARM is riskier than fixed rate. This is the general notion and with good reasons. With an ARM, the interest rate risk is passed on to you by the lender and with the US economy seen an almost zero interest regime for a long time now, the long term outlook could very well be higher interest rates.

*The fixed one comes with the peace of mind, and leaves you with easier refinance decisions in future if the interest rates go down further. *