"That’s alright, Br’er Fox - hang me if you gotta.  But please, please don’t fling me in that briar patch" - Br’er Rabbit to Br’er Fox in Disneyland’s log-flume attraction, “Splash Mountain”

The quote above is from one of my favorite rides at Disneyland, and it takes place after Br’er Rabbit has been trapped by Br’er Fox, which is right as the attraction riders are going up the slope. Then, the riders experience that thrilling (or in my case, terrifying) sensation of falling down the flume into the briar patch. This going over the falls is meant to symbolize the fact that Br’er Fox “took the bait” and did exactly what Br’er Rabbit wanted (but said would harm him), which was to get thrown into the briar patch so that he could escape.   

The ride ends with Br’er Rabbit running back to his “laughing place” and Br’er Fox fending off a hungry Br’er Gator (and the rider being typically soaked). Br’er Fox ultimately was tricked because he did not know that Br’er Rabbit was at home in the briar patch and would be able to escape if thrown there.

If you have ever ridden this ride, you may have thought “How could Br’er Fox fall for a trick like that from an adversary?” The trick seems obvious. However, the truth is that we are being told “don’t fling me in that briar patch” on a regular basis, and we don't even know it. “Where is this happening?” you might ask. When banks encourage people to get a 15 year mortgage rather than a 30 year mortgage.

What is the Trick?

You are now asking yourself, “Huh? How is this a trick?” Well, let me explain. I was recently driving in my car and an advertisement came up from a lending company. The advertisement raved about how great a 15 year mortgage was compared to a 30 year mortgage for a borrower because of how much less interest the borrower has to pay. One important fact that struck me funny is that the less interest the borrower pays, the less interest the lender/bank receives. Does it seem strange that a lender would make an offer that helps the borrower, but hurts the lender? Do you think that it is possible that they are taking a page from the “Br’er Rabbit Playbook”?

To better understand what I mean, let’s look at this example.  Let’s assume that you chose a home that you would like to buy, and you will be taking out a mortgage of $100,000.  The mortgage banker gives you the option of either:

  1. a 30 year mortgage at 4% with monthly payments of $477.42 or
  2. a 15 year mortgage at 3% with monthly payments of $690.58.

You have to choose which is better for you, but the problem is that this is an “apples and oranges” comparison, as all of the variables are different (length of loan, interest rate, monthly payments) and you can’t bring it down to one common denominator. This makes the comparison between the two very challenging.  

How Does the Lender Pitch the 15 Year Mortgage?

Back to the commercial that I heard. In this commercial, the lender attempted to bring the comparison to one common denominator. The commercial did this by saying that if you add up all of the the payments for a 30 year mortgage compared to all of the payments for a 15 year mortgage, in the 15 year mortgage you pay way less interest. Let’s see how their idea plays out.

The two loans break down as follows:

  1. 30 year mortgage: 360 months x $477.42 = $171,871.20
  2. 15 year mortgage: 180 months x $690.58 = $124,304.40

The advertisement was right, with the 15 year mortgage you pay nearly $50,000 less in interest over the life of the loan. Additionally, this means that the bank receives $50,000 LESS in interest as well. Now is the part where you should be thinking to yourself, “Why would the banks pay to advertise a product that results in them receiving a lot less money than they would otherwise?”  

The answer is that, while they are getting less money, they do not care! The reason that they do not care is because banks, unlike the general public, understand that the velocity of money is often more important than the amount of the money.  In other words, the time value of money (“TVM”) matters, and it MATTERS A LOT!!!

Four-Function Math Analysis Will Not Work

The often relied upon four-function math analysis done above, which entails adding all of the monthly payments together, and which incorrectly is relied on by both lenders pitching the 15 year mortgage AND many personal finance experts, is extremely flawed. The reason it is flawed is because it does not account for TVM. Rather, it takes a dollar spent to today and treats it the same as a dollar spent 1 month from now, 15 years from now and 30 years from now.  

Four function math assumes that all of the dollars have the same value and are therefore all the same dollar. However, here you cannot add up the dollars and treat them as if they are the same dollar, because they are NOT THE SAME DOLLAR!!!! Each dollar has a different value in relation to the time it is paid.  

To illustrate my point, would you be willing to lend me $100 today if I promised to pay you back $100 in 30 years (assuming that there was good collateral and you were guaranteed to get your money back)? Most likely your answer is “No.” The reason is because, even though they are both the same amount, they are NOT the same value. $100 today is much more valuable than $100 in 30 years because of TVM.  

What is Time Value of Money?

What is the time value of money, exactly?  First, let’s say what it is not. TVM is not the same thing as inflation. People often mix up TVM with inflation as things today usually cost more than they did in the past, which sounds like a similar concept to TVM.  However, inflation is simply the price of goods rising and the purchasing power of currency falling.

TVM is different.  TVM simply says that a dollar today is worth more than a dollar tomorrow because of the interest that you can earn right now on that dollar today that you cannot earn on the dollar you will receive tomorrow.

Using the example above, if you lent me $100 today for 30 years, I could earn interest on that $100 for the next 30 years, and I get to keep all of that interest. Then, at the end of 30 years, I give you back the $100 principal. The interest earned is what makes the $100 today so much more valuable than the $100 in 30 years.

How Do We Analyze the Situation?

Now you may be asking yourself, “Well then, how does one analyze this situation considering TVM?” Herein lies the problem. In school we may have heard about TVM, but were never taught how to account for it. Therefore, TVM is simply dusted under the rug when making financial decisions because people have no idea how it works.

However. there are a number of ways to look at this situation, but you need to know how to use a financial calculator, which, unlike a traditional calculator, is able to account for TVM. One of the ways to examine this situation is to look at the mortgages as if you were the party on the other side of the table, as in the lender, or the investor buying the mortgage from the lender. Do you think that there is a possibility that the lender from the commercial preferred that you selected the 15 year mortgage over the 30 year mortgage because it was in the lender’s best interest?  Maybe, just maybe...

Anyway, to analyze it from the lender/investor's perspective, we have to know how cash flow streams are valued.  (Here I have to give a disclaimer that I have never worked in a bank, so I have no first-hand knowledge of behind closed door conversations of banks valuing mortgages. However, I invest in notes and understand how cash flow streams are valued, so I feel confident in speculating that banks do the same.) Cash flow streams typically are NOT valued by adding all of the payments together. Rather, the typical way to value a cash flow stream (or to bring them to one common denominator) is to determine the stream’s “present value.” What I mean by “present value” is what would an investor pay in cash money today to receive the right to get the cash flow streams.

So, what we will do to determine the present value is look at both cash flow streams for a 15 year mortgage and a 30 year mortgage, and figure out how much a bank/investor would pay for each of those cash flow streams if they wanted a 12% return (12% is simply an arbitrary number here, but I figure it is a good guess for a bank’s/investor’s desired return.  If you want to pick a different number, that is fine, simply make sure that you use the same number for both the 15 year and 30 year mortgage.)

To determine the present value, we need to use the financial calculator, and I will show you which buttons to push. If you don’t have one, no worries, simply follow along and everything will be explained.

First, let’s examine the 15 year mortgage.

15 Year Mortgage: (buttons to push in your HP 10bii financial calculator)

N (number of months) = 180 (180 months in 15 years)

I/YR (interest rate/year) = 12 (Like I said, this number you can fill in what you like. I am going to assume for this example that a note investor would want to make their money work at 12%, but if you believe it is another number, simply insert that number. One important note is that whatever number you use for the 15 year loan, the same has to be used for the 30 year loan as we want to bring this down to one common denominator)

PV (present value) = ???  (This is what we are solving.  We are working to determine how much a lender/investor would pay cash for this cash flow stream)

PMT (monthly payments) = 690.58 (These are the monthly payments received)

FV (future value) = 0 (The loan is fully amortized, meaning that after 180 months it is paid off)

After entering all of the numbers above and pressing “PV”, the present value is $57,540.27.  Meaning that an investor who wants their money to earn 12%, would pay $57,540.27 today in cash to receive the cash flow stream of $690.58/month for 180 months.

Next, let’s see how much an investor would pay for a 30 year loan.

30 Year Mortgage: (buttons to push in your HP 10bii financial calculator)

N (number of months) = 360 (360 months in 30 years)

I/YR (interest rate/year) = 12 (Has to be the same as the 15 year mortgage above as we are making this “apples to apples”)

PV (present value) = ???  (This is what we are solving. We are working to determine how much a lender/investor would pay in cash today for this cash flow stream)

PMT (monthly payments) = 477.42 (These are the monthly payments received)

FV (future value) = 0 (The loan is fully amortized, meaning after 360 months it is paid off)

After entering the above numbers, the present value is $46,413.98.  Meaning that an investor, who wants to make their money work at 12%, would pay $46,413.98 in cash today to get the cash flow stream of $477.42 for 360 months.  

What Does This All Mean?

Now, I know that there are a lot of numbers being thrown around, so let’s examine this from a “30,000 feet above ground” perspective.

To summarize, in the 15 year mortgage, an investor would receive $124,304.40 total over the life of the loan, and they would pay $57,540.27 in cash today to get that payment stream. While, with the 30 year mortgage, they would receive $171,871.20 (nearly $50,000 more than the 15 year mortgage) total over the life of the loan, but would only pay $46,413.98 ($11,000 less than the 15 year mortgage) in cash today to get the payment stream.  In other words, the 15 year mortgage is more valuable to a lender/investor.  So, if it more valuable to the lender/investor, it is more “expensive” to the borrower.

Below is a chart breaking down the numbers from the perspective of the bank:

 15 Year Mortgage30 Year MortgageWhich is Greater?
Total Received$124,304.40
$171,871.20
30 Year by $47,566.80
Present Value$57,540.27
$46,413.98
15 Year by $11,126.29

This literally make no sense!!!  Why would a lender/investor pay $11,000 more today to receive a cash flow stream that will ultimately give them $50,000 less? The answer, as you have probably gathered from reading thus far, is TVM.  

However, how does TVM play out here? It plays out that lenders/investors get their money back much faster with a 15 year mortgage than a 30 year mortgage.  As they get their money back much faster, they get the opportunity to put their money back “to work” by reinvesting it. Conversely, for the 30 year mortgage, they have to wait longer to put their money “to work” and that is lost opportunity costs that the lender/investor suffers.

For example, if the bank chooses the 15 year mortgage, it can get $1 back today and invest it at 12% interest, and in 30 years that $1 will turn into $35.95! However, for the 30 year mortgage, it has to wait a lot longer (sometime as long as 30 years) to put the dollar “to work,” thereby losing all of that interest. So, even though the lender gets less money with the 15 year mortgage, it can put the money to work faster, thereby resulting in more money being earned in interest than if the bank waited to get the money from the 30 year loan.

Essentially, in this situation, the 15 year mortgage is MUCH more valuable than the 30 year mortgage for the lender/note investor because they get their money back much faster. Conversely, for the borrower, who can make their money work at 12%, the 15 year mortgage is “more expensive” to them than the 30 year mortgage in today’s dollars, even though they pay less over the life of the loan.

What Does this Mean for You?

After this huge discussion and all of these numbers, what does this all mean for you?  There are two main lessons to gather from this example.  

First, the velocity of the money is often more important than the amount of the money. As shown above, the sooner one receives (or has to pay) a dollar, the more valuable that dollar becomes. This concept has a huge impact on the financial decisions that you face in your life. You have to account for time when dealing with investing and with finances.  

Second, you cannot rely on what the party “across the table from you” says to determine what is in your best interest. To not be reliant on the party across the table, you need to become educated on the principles of money, like time value of money. If you do not become educated on the principles of money, you will be stuck relying on what the other party says to make your decisions. Becoming educated in the principles of money is essential for your financial well being.  

So, become educated on the time value of money, so that you don’t end up in a position where you have to rely on a bank to tell you what is in your best interest. If you have to rely on the bank, then you will likely do the same as Br’er Fox did when relying on the “advice” of Br’er Rabbit, and we know how that ride ends.

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