Q: My wife and I recently purchased a new home and avoided mortgage insurance by taking a piggyback: Our first mortgage is a five-year interest-only adjustable-rate mortgage (ARM) for $296,000 at 5.375 percent for 30 years. Our second mortgage is a 15-year fixed-rate mortgage (FRM) for $55,000 at 7.01 percent. Our cash flow allows us to pay more than the interest on the ARM and the full payment on the FRM. Should we apply the excess to the ARM or to the FRM?

A: The general rule is to pay down the higher-rate debt first, which is the second mortgage. If both mortgages were FRMs, this would be a no-brainer; you would allocate all surplus cash to the second until it was paid off. The same is true when the first mortgage is a five-year ARM and you confidently expect to be out of the house within five years.

On many piggybacks, the first mortgage is fixed and the second is adjustable with a higher rate. In this case also you would channel excess cash flows toward the second.

But if the first mortgage with the lower rate is adjustable and your time horizon extends beyond the first rate adjustment, or if you are uncertain about it, the decision is trickier. While you should start by paying down the higher rate second, if market rates spike during the first five years, the rate on the ARM could jump by as much as 5 percent at the first rate adjustment, which would bring it to 10.375 percent. In that case, at some point before the rate adjustment, you should start paying down the ARM.

I can’t tell you exactly when to do this; you will have to rely on your gut. But your gut needs to be kept informed regarding the ARM rate expected at the first rate adjustment. This is easy to do but you must know the index used by your ARM, the margin, and the caps, all of which are shown in your note.

The expected rate at the first rate adjustment is the most recent value of the index, plus the margin (which doesn’t change), subject to caps. Usually the rate on a five-year ARM cannot increase by more than 5 percent at the first adjustment. As the index changes over time, the expected rate changes correspondingly.

If the expected rate climbs above the rate on the second mortgage, you have to think about whether and when to switch gears. The case for the switch gets stronger the higher the expected rate and the closer you get to the ARM rate adjustment.

Invest In Roth IRA or Mortgage Repayment?

Q: I have $500 a month available for investment. Should I put it in a Roth IRA, or use it to repay principal on my 6.5 percent mortgage? I am 35 years old and in the 33 percentile tax bracket.

A: I would put the maximum contribution of $4,000 a year in the Roth IRA, invested in a diversified portfolio of common stock, and use the remainder to pay down my mortgage balance.

Repaying a mortgage is an investment with a yield equal to the mortgage interest rate. Since you can deduct one-third of the interest from your taxes, you save only two-thirds of the interest when you repay the loan. Your after-tax yield is thus 6.5(1 – 0.33) = 4.33 percent.

Roth IRAs pay no taxes, but even so, funds invested in low-risk assets won’t do much better than 4.33 percent today. At age 35, however, you should not have a conservative IRA portfolio. I would put the IRA in an indexed common stock fund, which should yield 9 percent or more over the next 30 years, with no taxes due on it ever. Since your contribution limit is $4,000, use the balance to pay down your mortgage.

The writer is Professor of Finance Emeritus at the Wharton School of the University of Pennsylvania. Comments and questions can be left at http://www.mtgprofessor.com.

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