# Category: Loans and Debt

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## The Rule-of-78s : The Formula and How It Works

Outside of banking circles, the Rule-of-78′s is little understood, even though it is commonly applied to many consumer and business loans. For the borrower, it tends to have a pernicious effect in the nature of a hidden prepayment penalty. The borrower’s disadvantage is heightened by the fact that the operation of the Rule-of-78′s is often referred to as a "Rebate of the Finance Charge." Any consumer who heard the word "rebate" is always tempted to say, "Where do I sign?"

### Not so fast!

Here’s how it works: The name comes from the sum of the numbers one through 12, there being 12 months in a year. Yes, that adds to 78.

The theory of the Rule-of-78′s is that at the moment a borrower signs the Note, the borrower is immediately obligated to pay back all of the principal and ALL of the interest that will accrue in the future over the agreed term of the loan.

Now, if the borrower prepays, the lender "generously" forgives some of the interest EVEN THOUGH at the time for it to accrue has not yet elapsed and so that additional interest has not been earned. That’s the so-called "Rebate." Lenders argue that the uncertainty created about an early payoff entitles them to some compensation for being at the borrower’s whim for payoff. In a time of falling interest rates, that argument may have more merit than when interest rates are rising as the lender gets to put the money back to work at a higher rate and earn more.

In any event, the Rebate is calculated by summing the number of payments elapsed in inverse order as a numerator for the fraction in which the sum of the term is the denominator. That fraction times all interest over the life of the loan is the amount earned by the lender.

### Watch this example:

Assume a two-year loan (so we’ll assume the numbers 1 through 24) for $10,000 with interest at 12% per year. Using our online amortization schedule calculator, we know the monthly payment is $470.73. The amortization schedule’s "Running Totals" also tells us that over the life of the loan the total amount of aggregate interest to be paid would be $1,297.56 (when the "1st payment date" is one month after the "loan date").

After the fourth month, our borrower reaps a windfall and wants to prepay the whole loan. The fraction of the total interest earned by the lender is:

(Sum 24 to 21) over (Sum 1 through Sum 24)

90/300 = 30%

Now, let’s compare that to the interest actually paid to date to see what the penalty will be. From running the "Loan Table" module, we found the total interest to be $1,297.65 and the interest paid after four payments is $377.61, so the penalty is:

Earned Interest Per Rule: (30%) ($1,297.65) = $389.30

Interest Paid to Payoff: $377.61

Additional Interest Owed: $11.69

Maybe that doesn’t look like too big a number, but it’s an additional 3.1% interest. Had this been a $100,000 loan, the increased penalty works out to ten times as much, $116.84.

Paying off at different times for different maturities and different interest rates produces differing penalty sizes. Two general rules of thumb can be deduced:

1. The higher the interest rate, the greater the penalty amount.

2. The earlier the prepayment in relation to the term, the greater the penalty amount.

So if you’re a lender, you should love using the Rule-of-78′s. If you’re a borrower, you should try to avoid it. A caution for lenders: Some states have usury and other laws that may limit use of the Rule-of-78′s.

©, Morris A. Nunes. All rights reserved.

**NOTE:**

a) This paper may be freely published provided that the above copyright notice is attached along with the appropriate byline. Portions may be quoted for illustration purposes.

b) Contact Mr. Nunes

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## 3 Easy Ways to Save on Your Next Loan : Why pay more than you need to pay?

According to the Urban Institute, originations for first mortgages totaled $1.8 trillion in 2017. In addition, NADA (National Automobile Dealers Association) reports that in the United States, the nation’s 16,802 franchised dealers sold 17.14 million new vehicles in 2017, and total new-vehicle sales topped $1 trillion. If as in years past, approximately 70% of these new car purchases were financed, total new debt for new passenger car purchases would be approximately $700 billion. With the total value of new debt in these two categories exceeding $2.5 trillion for 2017, and assuming an average interest rate of only 5%, debtors will pay over $125 billion in annual interest carrying charges alone for just their single-year new purchases of homes and automobiles. The enormity of these amounts leads to a simple question:

Is it possible for borrowers to reduce their debt service costs? And if so, how?

The answer to the first question is certainly “yes.” The answer to the second question is…”that depends.” Since there are a number of techniques that can be used to reduce loan carrying costs, an individual needs to consider which method(s) is(are) best for him or her. This White Paper will discuss three self-help approaches that can be used to reduce the cost of almost any loan 1) simply, 2) without the borrower’s incurring any special ‘setup’ fees, and 3) without the need to consult a financial advisor or seek an advanced degree. The three methods are the accelerated payment (or extra principal payment) method, the initial short period method, and the fixed principal payment method. (Other techniques that can often be used will be discussed in a subsequent paper; they include the accelerated bi-weekly payment method and prepaying the next period’s principal.) The first of our current methods is widely known (although not necessarily well-understood) and can be implemented at any time during the course of paying off a loan. The latter two techniques can only be initiated during the loan application process, or shortly after origination (and, in either case, before the first payment is made).

## Accelerated Payment Method

The first cost reduction technique is the “accelerated payment” method. Our first example may seem trivial to some, but it clearly illustrates how making a small extra principal payment, along with the regular payment, can reduce the consumer’s cost of carrying a debt. For illustration purposes, assume that a car is financed for $13,000.00, payable over 48 months, at 11% interest. A loan calculation shows that a monthly payment of $335.99 is needed to amortize completely this loan. Total interest paid over the 48 months will come to $3,127.60. Now assume that, once the borrower has recovered from the initial costs of making the purchase (insurance, down-payment, title, etc.), he or she can set aside an extra $50.00 a month toward repayment of the car loan. After the 6th payment, the consumer sends the lender an extra $50.00 a month, with instructions that the funds be applied to reduction of the principal. This extra monthly payment of $50.00 is then continued until the loan is paid off. Thus, for the first extra $50.00 principal payment, the borrower saves the interest that would have been owed on the $50.00 for the next 42 periods (approximately $19.25 for the single $50.00 payment over the remaining 3.5 years). Each subsequent extra payment saves the interest that would have been due on that amount for each of the remaining periods.

The cumulative effect of these modest extra payments can be significant. In this particular example, the savings add up to $384.19. While this may not seem like much (then again, neither is $50.00, but hey, it’s your money), it represents a savings of slightly more than 12% of the cost of the loan. What’s more, the loan is paid off over six months earlier than would otherwise be the case. The next example is far more dramatic.

Our next illustration assumes a $250,000.00 mortgage, taken out for 30 years, at 6.0%, with monthly payments of $1,498.88. Alas, total interest alone paid over the 360 months will typically come to $289,593! What would be the savings if an extra $250.00 were applied to principal each month, starting in say, the 13th month? In gross terms (i.e., before taxes), the interest savings will equal about $92,393, and instead of the loan being paid off with the 360th payment, it will be paid off after the 257th payment (that is, after 21.4 years instead of the standard 30 years). Thus, the mortgage is shortened by nearly 9 years.

What can be learned from these two examples? Firstly, that even a small increase in the monthly payment can save the consumer a significant percentage of the cost of carrying a loan. Secondly, that the longer the term of the loan and the earlier the extra payment starts, the greater the savings for the borrower. In the first example, the extra payment equals about 15% of the regular payment and commences after 12% of the payments have been made. As indicated above, the result is that the borrower saves about 12% of the cost of carrying the loan. In the second illustration, the extra payment is just about 16.6% of the regular payment, but commences when only about 3% of the payments have been made, resulting in savings that exceed 30% of the potential loan costs. Note also that, if the interest rate on the mortgage were equal to that of the car loan, the savings would be even greater. Therefore, we can also conclude that the higher the rate of interest, the greater the achievable savings from prepayment.

## Short Initial Period Method

The next cost reduction technique we will examine is the “short initial period” method, an approach that many people can put to work almost painlessly. As the name suggests, this option is available to borrowers at or near the origination date of the loan. Consider, for a moment, the payment schedule of a typical consumer loan. Many such loans are set up with a monthly payment due on the first of each month. The borrower, however, almost never receives the proceeds (funds being borrowed) on the day of the month corresponding to the payment due date. For example, if the loan closes or the funds are advanced to the borrower on April 10th, it is said that the origination date is April 10th. The lender will most likely state that the first payment is due on June 1st. In cases like this, the loan has what is referred to as an “initial long period,” i.e., the first period is longer than the regular payment period. (In this case, the regular period is one month.) Don’t worry though, the lender isn’t granting the borrower use of the money without collecting interest! Assume, though, that the borrower has the first payment already set aside. After all, few mortgage lenders will even make a loan unless they know that the first couple of payments are available in a bank account. Therefore, what would be the effect on the cost of the loan if the first payment were made on May 1st instead of June 1st?

Surprisingly, the savings are very significant. Citing the same mortgage illustration that we used above ($150,000.00 mortgage, for 30 years, at 8.5%, with an origination date of April 10th of any year), if the first payment is made on June 1st, which is when most lenders will ask for it, the total interest paid on the loan will be $265,957.27. If, however, the first payment is made on May 1st instead, the total interest cost drops to $261,231.93. The savings exceed $4,700.00, simply because the borrower starts to pay back the loan one month early!

Now, let’s take this illustration one step farther. Suppose the borrower makes the first payment on April 11th. What do you suppose the savings will be? If moving the first payment date up by thirty days saves a little more than $4,700.00, then moving it up another 20 days or so should save, maybe, the better part of another $4,000.00, right? Wrong! If the first payment date is advanced to April 11th, the total interest paid over the term of the loan is reduced to $252,714.43, for a savings of over $13,200.00 compared to the typical first payment cycle, and over $8,500.00 compared even to a May 1st payment date! Granted, in percentage terms, this doesn’t save the consumer all that much: ‘only’ about 5% of the cost of the loan. But 5% of a big number is still a big number! Many people will feel that, in absolute terms, saving over $13,000.00 by simply moving the payments ahead by a month-and-a-half or so is not only worth doing, but tantamount to ‘money-in-the-bank.’ This is especially true if the modest amount required to initiate the tight first payment cycle is readily available or can somehow be cobbled together. The reader should note that achieving these savings does not require a restructuring of the loan. Nor does it require the borrower to subscribe to a special ‘cost reduction plan’ that some lending institutions offer. Also, it is not necessary to enlist the aid of an accountant or financial planner. In other words, the consumer does not have to go to much trouble, or pay for any services, in order to save real cash.

[Note on Payment-in-Advance for the Advanced Reader]

Some readers may be wondering why this last illustration didn’t suggest that the first payment be made on the origination date instead of one day after the origination date. It certainly could have been made then. Employing this calculation, however, tends to produce a result that appears quirky and counter-intuitive. At first glance, the savings will probably seem to be less than the savings made by starting the payments on April 11th. How can this be? You might say that this is due to an idiosyncrasy in the way most loan calculation routines work.

Actually, what is happening is very simple. Almost all loans are set up using a method called “payment-in-arrears.” This simply means that a lender lends a borrower some money and then, at some point in the future, the borrower starts to make payments to reduce the outstanding principal balance. The reason that the standard method is known as payment-in-arrears is because the borrower starts to make payments after he or she has had use of the money. (It does not mean that the borrower is in arrears or late with respect to the loan’s payment schedule, an unfavorable status known, of course, as “delinquency.”) In contrast, when the first payment is made on the origination date of the loan, the borrower has yet to have use of the loan proceeds when a payment is made. This concept is known as “payment-in-advance.” (Incidentally, leases typically use the payment-in-advance calculation method, and this is one of the ways lessors can achieve an apparently ‘low’ monthly payment amount; on closer examination, however, it is the lessee who is supporting the low monthly payment!)

A loan calculation program should recognize a loan that is based upon the payment-in-advance method when the origination date equals the first payment date. It will then calculate the payment using this different method, which is why the savings will appear to be less than the savings made by starting the payments one day after the loan origination date.

The reader should also note that, in the above mortgage illustration, if the loan is paid-in-advance, the payment drops from $1,153.37 to $1,145.26. This happens simply because the lower number is the payment amount required to amortize the principal over the entire term using the payment-in-advance method. When a loan calculation program sees that the first payment is one day after the origination date, it assumes a loan-in-arrears, which it is, and that the first period, while short, is indeed a full period. Thus, the payment amount is not adjusted but, because the first period is so short, most of the first payment is applied toward principal and the loan is accelerated.

Our payment-in-advance model goes to show just how much difference an $8.11 swing in the monthly payment amount can add up to over 30 years. In fact, the payment-in-advance method does save the borrower about $3,000.00 over the traditional payment-in-arrears loan when the first payment period is a full period or longer. Therefore, when invoked as an alternative to a traditional loan payment schedule, payment-in-advance can also be considered an actionable acceleration technique. Additionally, it has the benefit of reducing the periodic payment slightly. (If you wanted to see what the interest-cost reduction effect would be if a payment-in-advance loan were liquidated using the same payment amount as if paid in arrears, you would use an advanced loan calculation program that allows the user to override the calculated payment amount.)

## Fixed Principal Payment Technique

The third and final loan acceleration technique covered in this presentation may require the borrower to shop around, or negotiate a little, in order to get it set up. Up until this point, we have only discussed loans that have level periodic payments, i.e., payment amounts constant from period-to-period (save, perhaps, an odd final payment). When a level payment amount is used, the interest due is calculated, then deducted from the payment. If there is anything ‘left over,’ the remainder of the payment is applied toward principal. As each payment is made, the amount of interest due decreases and the amount applied toward reduction of the loan’s principal increases.Our technique, called the “fixed principal amortization” method, is characterized by a level principal payment (as opposed to the standard, level periodic payment, made up of both principal and interest), with the interest for each period added to the principal payment. The formula used to calculate a fixed principal payment mortgage is different from the formula used to calculate a level periodic payment mortgage. Using the mortgage example that we have employed above, the principal amount is divided by the number of payments (here, 360). In doing so, we find that 1/360th of the $150,000.00 principal amount is $416.67. Thus, $416.67 becomes the base for the payment. The interest for each period is added to this base amount to calculate the entire payment amount. (Remember that, for level payment loans, the interest is deducted from the payment.) This math results in a periodic payment that is not level because, as the principal is reduced for each period by $416.67, the amount of interest due declines, so less and less interest is added to the $416.67 base payment over the term of the mortgage.

The reader should note that, with a fixed principal payment loan, the payment is initially somewhat higher than for the more traditional level periodic payment loan, in this case by about $321.00, or 28%, at the first month. In fact, it is not until the borrower has made payments for a little more than 10 years that the payment amount finally drops to that of the traditional mortgage. This is because the fixed principal payment loan’s higher payments have reduced the mortgage’s balance by nearly $33,000.00, or 25%, more than have the 120 level payments on the traditional mortgage. Once the 10-year mark is reached, however, the payments quickly decline. By the end of the loan, the monthly payment is well below $500.00, or less than half of the $1,153.37 regular payment under a traditional mortgage payment schedule. Understandably, handling a higher-than-required monthly payment in the early years is often difficult for a first-time home-buyer. As a result, the fixed principal payment technique may be best initiated by a more seasoned mortgagor, for instance, one who is ‘rolling over’ the proceeds of an appreciated home and can comfortably live with higher payments for the first few years. For such a veteran home-buyer, even these new, fixed principal monthly payments can be lower than the level periodic payments on his or her previous home. The best part is that this loan acceleration technique has a great payback. The total interest saved is almost $74,000.00, or nearly 30%, of the financing cost of the loan!

## From Just Whose Pockets Will Your Savings Come?

Most lending agreements allow prepayment without penalty, especially after the first year. A lending institution will tend to sell most mortgages, and often, even unsecured debt, in the secondary market. This practice allows the loan’s originator to turn over its capital, thus freeing up funds with which to underwrite new loans; as part of this business approach, the lender may retain the loan’s lucrative servicing functions.

When a borrower redeems a mortgage early, whether by one day or a number of years–or saves carrying costs by any of the other methods we have addressed in this report–the consumer’s savings are likely to come from the bulging pockets of passive investors who have acquired an interest in a mortgage or loan portfolio. In a declining interest rate climate, early loan redemptions will have the effect of lowering the average yield on investors’ portfolios. In a market of rising rates, investors will gladly reinvest their portfolio proceeds in higher-yielding securities. But no matter what the interest rate environment, rest assured that the original lender, and any subsequent investors, have earned a fair return on the borrower’s loan for the period it remained outstanding.

While these debt service cost reduction techniques are not for everyone, borrowers should be aware of different strategies that they can employ–even insist upon–to reduce their costs. Many banks and finance companies, and mortgage banks and brokers, will accommodate custom loan packaging requests if asked, but will not volunteer them simply because they represent ‘exceptions’ to the path of least resistance. Clearly, lenders wish to sell their most profitable, lowest overhead products. Also, many borrowers, especially first-time home-buyers, tend to be impatient, insecure, or reluctant to push for the terms they really need. But if consumers can manage the uncertainty and stress of major purchases, and reduce their effective carrying charges by just a few percentage points on every loan, there will be millions of well-rested people, and billions of dollars available, for productive uses in our economy.

Notes:

a) This paper was originally written and published by Karl Thompson. The author is grateful for the editing by Mr. Marlow.

b) This paper may be freely published provided that the above copyright notice is attached, along with the appropriate byline. Portions may be quoted for illustration purposes.

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