A reader writes in, asking:

“I have been making sure to make my mortgage a priority the last few months because I realized that is the highest paying fixed income investment I could invest in at the moment because I understand how to compare it to the yield on typical bonds. But when I compare to I bonds, how do I perform this comparison? For example, on the I bonds issued between May and November of this year…is it better to pay my 3.125% mortgage or invest in these I bond issues with composite rate 3.54%, fixed 0%?”

### Comparing Risk

As a bit of background information for readers not familiar with I Bonds, their interest rate is made up of two components: a fixed rate and a variable rate.

The fixed rate stays the same through the life of the bond. For I Bonds purchased right now, the fixed rate is 0%.

The second component is a a variable rate that gets recalculated every 6 months, based on the rate of inflation over the prior 6 months (specifically, the change in the Consumer Price Index for all Urban Consumers). For I Bonds purchased right now, the variable rate is 3.54%.

So, today, when we see a 3.54% composite rate, made up of a 0% fixed rate and 3.54% variable rate, we only know that that variable rate will be applicable for 6 months. After that, it could be lower or higher, depending on inflation.

In contrast, if the mortgage is a regular fixed-rate mortgage, we know what the rate of return will be (i.e., the after-tax rate of interest that you no longer have to pay).

Of course, that’s in nominal terms. In *real* (i.e., inflation-adjusted) terms, it’s the I Bonds that have the predictable rate of return (in this case, 0%, minus any tax you would have to pay on the variable rate), whereas the mortgage has an unpredictable rate of return (i.e., the rate on the mortgage, tax-adjusted, minus whatever inflation turns out to be).*

### Comparing Returns

In both cases, we want to look at the after-tax rate of return.

If your mortgage interest is fully deductible, we would multiply the interest rate by 1 minus your marginal tax rate (federal + state, if you can deduct the interest at the state level as well). For example with a 30% marginal tax rate, paying down a 3.125% mortgage would provide a nominal after-tax rate of return of 2.1875% (i.e., 3.125% x 0.7).

And you would also want to adjust the interest rate on the I Bonds accordingly. I Bonds are generally taxable at the federal level. But they are exempt from state income tax. In addition, if the bonds are ultimately used to pay higher education expenses, the interest will be federally tax free as well.**

In short, there’s going to be a break-even rate of inflation at which you are indifferent to prepaying the mortgage as opposed to buying I Bonds.

If taxes were not a consideration, that would be 3.125%. (That is, if inflation is 3.125% over the period in question, both I Bonds with a 0% fixed rate and prepaying a 3.125% mortgage would have a 3.125% nominal return or a 0% real rate of return.)

Considering taxes, we’d want to do some algebra in which we set the real rate of return on the mortgage equal to the real rate of return on the I bonds, and solve for inflation.

That is:

- mortgage real rate of return = I Bonds real rate of return

The mortgage real rate of return can be written as:

- after-tax mortgage interest rate
**−**inflation.

And the real return for the I Bonds can be written as:

- fixed rate
**−**taxes paid on fixed rate + variable rate**−**taxes paid on variable rate**−**inflation

For I Bonds purchased today, the fixed rate is 0%. And the variable rate will always be equal to inflation. So we can rewrite the real rate of return for I bonds purchased today as:

- 0
**−**0 + inflation**−**(inflation * marginal tax rate)**−**inflation

Or simply:

**−**(inflation * marginal tax rate)

For example, if the mortgage has a rate of 3.125% and you expect a 30% tax rate on the mortgage and a 22% tax rate on the I Bonds, the break-even rate of inflation would be 2.804%.

- mortgage real rate of return = I Bonds real rate of return
- 3.125% * 0.7
**−**inflation =**−**0.22 * inflation - 2.1875%
**−**inflation =**−**0.22 * inflation - 2.1875% = 0.78 * inflation
- inflation = 2.804%

That is, with inflation of 2.804% and a 30% tax rate on the mortgage and 22% tax rate on the I Bonds, they each provide the same after-inflation, after-tax rate of return.

Mortgage real rate of return = 3.125% * (1 **−** 0.3) **−** 2.804% = **−**0.617%

I Bonds real rate of return = **−**0.22 * 2.804% = **−**0.617%

If you expected inflation greater than 2.8%, I Bonds would be expected to provide a greater after-tax return. If you expected inflation less than 2.8%, the mortgage would be expected to provide a greater after-tax return.

### Liquidity

Another important difference between using cash to buy I Bonds and using cash to pay down a mortgage is that buying I Bonds would preserve a greater degree of liquidity. You can cash I Bonds after one year. (If you cash them before five years, you lose the previous three months of interest.) Whereas when you pay down a mortgage, that cash is gone, and there is no cashflow benefit until the mortgage is paid off.

*Throughout this article I am using the simplifying convention of subtracting inflation from the nominal return in order to find the real return. The more precise math is to divide (1 + nominal return) by (1 + inflation), then subtract 1.

**For simplicity’s sake, I am ignoring the fact that with I Bonds you have the choice to pay tax on the interest each year or defer taxation until the year in which you cash the bond or the bond matures. In theory, deferral is an advantage. But the specifics will depend on how your marginal tax rate changes over time.