How do I figure out if I can get ahead by earning 6% if I have an 8% loan?

At first glance, the answer is obvious, you don’t get ahead.  However, sometimes we get confused and think that since an account (say at 6%) has an increasing balance while a loan (say at 8%) has a decreasing balance, we might be able to get ahead.  Let’s look at it to see the whole truth of the matter.

Take a \$100,000 account earning 6% over 20 years.  Future Value: \$320,714.  We know it earned \$220,714 worth of interest.  This is calculated by taking the  \$320,714 total and subtracting the \$100,000 initial investment.

Now let’s look at a loan for \$100,000 at 8%. We can see that our loan payment is \$9430.76 and if we multiply that by 20 years, we get \$188,615.20, so we know that we paid \$88,615.20 in interest.  So an incorrect deduction would be that it would make financial sense to have 6% earnings while we are carrying 8% debt, but this is only because all of the facts are not presented.  Let’s take a closer look.  The only way to make valid financial conclusions is to have exactly the same cash flows and time periods in each of the comparisons we are trying to make.

Under those guidelines, if we take the \$100,000 and pay off the loan at 8%, then take the payments of \$9430.76 that we no longer have to make loan payments of and pay them instead to the 6% account, in 20 years, we have \$367,731, instead of \$320,714 in the earlier example. So while it is true that we pay less interest (\$88,615.20) than we earn (\$220,714), that is only part of the truth.  The whole truth is that cost of money does matter and in the above example, our costs are greater than our gains.  This is the whole truth, even though we earned more interest than we paid out in interest.  There is a \$47,017 improvement by paying off the 8% loan with the 6% account and redirecting the freed up payments to the investment.

One critical issue left over is liquidity.  Obviously \$100,000 in an account leaves us in a more liquid position initially than \$9430.76 being contributed to an account every year.  But eventually the investment account with \$9430.76 being added annually will over take the account with \$100,000 being contributed up front and will exceed it by \$47,017 in the 20th year.

So if initial liquidity is a concern, then it may be worth giving up some of the \$47,017 gain to be in a more liquid position.  However, it is not true that there is a mathematical advantage in having a higher rate of interest on your debt than on your earnings.