In reading a few blogs this week (some at Consumer Commentary, Free Money Finance and others), there has been a lot of discussion about the power of compound interest and about paying off college loans and mortgages early due to paying too much interest to the bank. It got me to think that a lot of articles are written covering one of three parts (i) interest paid to banks, (ii) compounded returns on investments and (iii) inflation; yet, only occasionally are all discussed together to see the interactions of each. Unless the numbers that are presented together; the results are incorrectly skewed in my mind. It can be a marketing magic trick that shows us only ½ the picture to influence us to use their services with inflated numbers. Other times it is done in pieces because it is difficult to show everything together (as you will see based on my attempt).
Let’s start easy. If you have $20,000 and invest it at different investment returns, it would grow over 20 years to approximately:
• At 3.5% – $40,000
• At 5.0% – $53,000
• At 8.0% – $93,000
• At 10.0% – $135,000
One would look at $135,000 and say “Wow, this is why I should be invested in the stock market.” Yet, before this goes too far, the first magic trick is showing numbers that have not been adjusted for inflation. For example, if you could buy something that is $20,000 today, it will cost $40,000 in 20 years assuming 3.5% inflation. In reality, the $40,000 return using 3.5% investment return is only worth $20,000 in today’s buying power. In addition, the $135,000 is only worth $68,000 in today’s dollars, still a significant increase but not as much of a “wow” as before.
In today’s buying power, the $20,000 investment would grow over 20 years to
• At 3.5% – $20,000
• At 5.0% – $27,000
• At 8.0% – $47,000
• At 10.0% – $68,000
That is some illusion of showing the power of compound interest and leaving out the point that a loaf of bread is going to cost $4 in 20 years instead of $2 today.
Now, let’s look the decision whether or not to prepay a mortgage (or other loan). First, the idea of prepaying a loan should be broken down into 2 parts:
• A decision to save the extra payment
• A decision where to invest (paying off mortgage or invest in CDs, bonds or stock)
If I have a $100,000 mortgage at 5% interest rate, I would have payments of $535. If I prepay the mortgage by paying $579.58 a month (44.58 more a month or $535 a year), I would payoff the loan in 25 years and 3 months. Yes, prepaying the mortgage would save $17,000 of interest. Yet, the $17,000 is only showing ½ the picture (which I will explain below) and the $17,000 in lost interest is equivalent to $9,000 in today’s dollars.
The other ½ of the picture is if you considered saving the extra payment and invested it in stocks, you may actually lose more money by deciding to pay off the mortgage instead of investing. If you had invested $44.58 a month (instead of paying off the mortgage), you would have after 25 years and 3 months the following (shown at various assumed post-tax returns and not adjusted yet for inflation):
3.5% – $22,000
5.0% – $27,000
8.5% – $47,000
10.0% – $61,000
If you saved at 5% rate, you would have earned enough to pay off the remaining mortgage of $27,000 at the same time that the prepayment plan would have paid it off. Thus, in my mind, prepaying a mortgage is like investing in bonds at your mortgage interest rate (ignoring taxes for now). So, the decision is in two parts:
• Whether to save an extra $44.58 a month – which would result in $22,000 using at 3.5% investment return rate (which is $9,000 in today’s dollars)
• Where to invest the money: either in money market at 3.5%, bonds at 5.0%, stocks at an estimated 8.5% to 10% return or by prepaying the mortgage
o Prepaying the mortgage will save an additional $5,000 which is the difference in 5% return and 3.5% return. In today’s dollars this is only worth $2,000 which is not very much compared to the $17,000 in interest saved
If you are a young investor (risk taker) and would invest a majority of your money in stocks (at an assumed 8.5% return), you could lose out on possibly $20,000 by prepaying the mortgage instead of investing ($20,000 = $47,000 assumed investment return – $27,000 remaining mortgage) and your mortgage would still have been paid off at the same time the prepayment plan would have been. So, by prepaying you may not being saving $17,000 of interest but losing potentially $20,000 or more depending on your actual investment return. Note, the $20,000 of potential return is equivalent to $8,000 is today’s buying power to compare apples and apples (because I do not want to appear like I am magically inflating numbers).
Now, there are a lot of reasons to prepay or not to prepay a mortgage. You can read more at:
Should I Have a Mortgage
Sometimes when people just look at interest that they are paying, they decide to prepay the mortgage after only seeing ½ of the total picture that does not even show results adjusted for inflation. So objects may appear larger than what they should and the illusion of seeing 1/2 the picture is an example of focusing our attention to one side of the room (savings) while the elephant (other investment options) is hiding on the other side. Thus before prepaying your mortgage sit down with a financial advisor to see the whole picture and get the numbers converted into today’s dollars so you are comparing apples and apples.
Some would say that prepaying a mortgage is a guaranteed return, which it is. For an older investor who wants to invest more conservatively due to his approaching retirement (e.g., invest more in bonds and less in stock), prepaying a mortgage may be a good option to look into with his financial advisor. Yet, for a young investor who is taking calculated risks due to a longer term investment horizon, it seems a little contradictory in my mind to say he would invest a majority of your money in stocks (which have a higher upside but no guaranteed return), yet prepay his mortgage for the guaranteed return. Of course, his overall risk analysis needs to be reviewed with his financial advisor because prepaying the mortgage is just one part of his investment plan. Yet, I am always a little cautions when someone tells me in one breath that a guaranteed return is always better (e.g., prepaying a mortgage) and then says that if I am younger investor with a long-term investment horizon that a large share of my investment should be in the stock market due to its potential higher returns.
For me, I am prepaying just little on my mortgage now for three reasons:
• I am getting a little older and have a large stock investment already, so I am looking to lower my overall investment risk (e.g., with bonds and prepaying my mortgage).
• I wanted my mortgage to be paid off by the time my son goes to college, so our income currently allocated to our mortgage can then be allocated to pay part of his college expense (with him paying the rest)
• My prepayment now less than the typical prepayment plan yet is going to increase over time so our home payments (including maintance and taxes) is consistently around 25% to 30% of our income
Note, the interest paid is not one of the reasons why I am prepaying my mortgage. My real decision is based on how much I want (need) to save and where to save it (e.g., equities, bonds, CDs or prepaying the mortgage).
Now, for the last point, I will attempt to discuss the effect of inflation on the interest charged on a loan. The premise is that for a low interest rate loan, a lot of the interest paid is due to inflation. For myself, I do not see this interest paid as lost money if it is due to inflation. It is just time value of money and does not constitute a loss of buying power. This may sound confusing because no one talks about it.
Let’s look at a scenario where a person has an outstanding loan of $10,000 due in 10 more years at 3.5% interest rate (3.5% being the assumed inflation rate):
• If he gets a windfall and invests it in CDs or mutual funds (safe investment) that provide a post-tax return equal to 3.5% (inflation) there is no loss of money if he pays if off now or later
Loan outstanding now – $10,000
Pay loan back – $14,000 in 10 years
Invest – $10,000
Investment grew to $14,000 after 10 years
Thus, his investment grew enough to pay back the loan and the decision to prepay the loan did not cost him anything. Now, many (if not all) will say that he is losing $4,000 in interest by not prepaying the loan back immediately. Yet, by saving the money in a secured investment, most if not all the costs of the low interest rate loan is eliminated. Plus, he has the money for an emergency if needed. So the money lost by not prepaying the loan is $0 even though he is paying $4,000 of interest . Sounds confusing I know. After years of hearing interest is always bad, it is hard to see the distinction between interest due to inflation and interest costs due to risk and investment horizon.
Well, what happens if he spent the windfall instead of investing the money? From a buying power perspective, the buying power is still not affected.
If the person’s salary is $50,000, the $10,000 loan is 20% of his salary.
If he waits 10 years to pay it off, his salary would normally increase to $70,000 (assuming 3.5% salary growth) and thus he would need to repay the loan $14,000 which is 20% of his salary ($14,000 / $70,000).
Thus, he did not lose any buying power at all due to his decision not to pay the loan of earlier. He could also pay the loan back 2% of his salary for 10 years as well. Thus, the money paid back on the loan is just from time value of money (inflation).
As you can see below, inflation affects everything over time (interest rates, investment returns and salary increases), thus to find the real costs (on an inflation adjusted basis) the inflation component should be removed from each to compare apples to apples:
Loan interest rate = Inflation + Risk + Investment Horizon (higher rate for longer loans)
Investment return = Inflation + Risk + Investment Horizon
Salary increase (in theory) = Inflation + Merit/Promotion + Productivity
Note, there should be a drive to pay back credit card loans, payday loans and other high interest rate loans as quickly as possible because they will rob you of overall buying power because they are charging an interest rate that dwarfs the long-term assumed inflation rate. Yet, low fixed interest rate loans do not rob you of as much buying power as interest charges suggest because most of the interest changed is for inflation which has minimum if an effect on your buying power. This is because your salary and investments are also increasing at a similar pace (over the long term).
One last example, let’s look at a student loan of $20,000 with 3.5% interest with his salary at $50,000. The person can pay the loan back now using 40% of his salary or pay it back over 10 years at 4% of his salary. From a buying power perspective, he is not losing anything (even though the interest paid is approximately $4,000). Yet, by amortizing the loan over 10 years, he makes it easier to payback the loan without killing himself in the first year.
To try to tie this all back together. If you have a loan that is repaid by at $115 per month for 20 years ($27,600 in total payments), the interest paid is at various loan interest rates is
• At 3.5% – $7,600
• At 5.0% – $10,100
• At 8.0% – $13,800
• At 10.0% – $15,600
From a buying power perspective, the loan at 3.5% has no effect on your buying power because it is the assumed long-term rate of inflation. Thus, lot of the interest paid on most standard loans low interest rate loans is due to time value of money (effect of inflation being $7,600). So if you have a mortgage at 5% or 6%, the marketing material for a biweekly mortgage plan can lead you to think that you are paying a lot of interest to scare you into their plan (for one-time fee of $300 with a small fee for each payment there after). Yet, the actual cost from a buying power perspective is less once inflation is accounted for.
So, my point is paying some interest is not that bad from a buying power perspective. Yet, this does not mean to load up with credit card and PayDay loans (at higher interest rates) or to have too much debt (as many are getting into trouble due to having to high of a debt burden).
In addition, when you look at numbers, see if the number can be converted to today’s buying power so you are comparing apples and apples. This way, you are not thinking that a $1 million today is equivalent to $1 million in 40 years when the average car will cost $100,000 (when the real value of $1 million is only $250,000).
And as always you should consult with a financial advisor to analysis your specific debt and risk situation.