In writing this piece I must admit that it is not the piece
I wanted to write. A colleague of mine introduced me to a service called the
Worth Account (www.worthaccount.com). I respect my colleague deeply, and while I wanted so badly to recommend his product as a way for consumers to beat their debt, I unfortunately cannot do so having scrutinized the math behind it.
Briefly summarized, the Worth Account is a computer program
that calculates the best combination and sequence by which to pay off an
individual’s total debt based on their income and the application of their
savings to paying off their debt ahead of time. It’s a program that one can
purchase for a variable price (based on the savings calculated over time with
its implementation), and can cost anywhere from a few hundred to a few thousand
dollars depending on one’s debt.
But…
Does their premise hold true?
Let’s look a little closer.
The basic premise of the worth account is that its
algorithms calculate the maximal amount of disposable income one can apply to
their debts as a whole, and then calculate the optimal allocation of said
disposable income to make extra payments towards those debts to pay them off
with a minimal amount of interest paid in the shortest amount of time.
I will not go into whether the Worth Account is actually
worth it or not as that depends on one’s debts, financial situation, income,
discipline, and propensity to save. Instead, let’s focus on payment methods.
There are essentially three ways to make a payment on a
debt. First, one can make a monthly payment with no extra payments towards
principal. Second, one can make an extra payment every month in addition to
their minimum payment. Third, instead of an extra regular monthly payment, one
can periodically make a large payment towards the principal at arbitrary
(regular or irregular) intervals, for example, applying one’s tax refund to
their mortgage principal, or paying the equivalent of the regular monthly
payments, but doing so quarterly, semiannually, or some other way.
While some may think that making biweekly payments or some
other partial payment scheme is also a possibility, banks typically do not
apply partial payments to the balance of the loan. Such payments are typically
held by the bank until a full payment is made, at which time such payment is
applied, or just returned to the borrower outright, effectively eliminating any
interest cancelling benefit perceived by the partial payment (http://www.thetruthaboutmortgage.com/biweeklymortgagepayments/).
Therefore, such schemes will be ignored for this article.
Most payment schemes will be variations of these three. Refinancing
and other types of borrowing from one source to pay off another will not be
covered in this article.
Take a hypothetical loan with the following parameters:

30 year fixed loan (360 monthly payments)

4.5% interest rate

$200,000 principal
The monthly payment on this loan will be $1,013.37 based on
its normal amortization.
After the first year, with no extra payments, the
amortization will be thus:
Payment

Principal

Interest

Amortization

Total Interest

Balance

1

200,000.00

750.00

263.37

750.00

199,736.63

2

199,736.63

749.01

264.36

1,499.01

199,472.27

3

199,472.27

748.02

265.35

2,247.03

199,206.92

4

199,206.92

747.03

266.34

2,994.06

198,940.58

5

198,940.58

746.03

267.34

3,740.09

198,673.23

6

198,673.23

745.02

268.35

4,485.11

198,404.89

7

198,404.89

744.02

269.35

5,229.13

198,135.54

8

198,135.54

743.01

270.36

5,972.14

197,865.17

9

197,865.17

741.99

271.38

6,714.13

197,593.80

10

197,593.80

740.98

272.39

7,455.11

197,321.40

11

197,321.40

739.96

273.42

8,195.06

197,047.99

12

197,047.99

738.93

274.44

8,933.99

196,773.55

Applying a regular monthly payment of $750 to the principal
will yield the following amortization:
Payment

Principal

Interest

Amortization

Total Interest

Balance

1

200,000.00

750.00

1,013.37

750.00

198,986.63

2

198,986.63

746.20

1,017.17

1,496.20

197,969.46

3

197,969.46

742.39

1,020.99

2,238.59

196,948.47

4

196,948.47

738.56

1,024.81

2,977.14

195,923.66

5

195,923.66

734.71

1,028.66

3,711.86

194,895.00

6

194,895.00

730.86

1,032.51

4,442.71

193,862.49

7

193,862.49

726.98

1,036.39

5,169.70

192,826.10

8

192,826.10

723.10

1,040.27

5,892.79

191,785.83

9

191,785.83

719.20

1,044.17

6,611.99

190,741.66

10

190,741.66

715.28

1,048.09

7,327.27

189,693.57

11

189,693.57

711.35

1,052.02

8,038.62

188,641.55

12

188,641.55

707.41

1,055.96

8,746.03

187,585.58

In this next case, comparative to $750 per month, we will
add $3,000 towards principal every four (4) months.
Just to ensure comparability, $3,000 x 3 payments (one every four (4) months of the (12 month) year) =
$9,000. $9,000 divided by 12 months = $750/month.
Payment

Principal

Interest

Amortization

Total Interest

Balance

1

200,000.00

750.00

263.37

750.00

199,736.63

2

199,736.63

749.01

264.36

1,499.01

199,472.27

3

199,472.27

748.02

265.35

2,247.03

199,206.92

4

199,206.92

747.03

3,266.34

2,994.06

195,940.58

5

195,940.58

734.78

278.59

3,728.84

195,661.98

6

195,661.98

733.73

279.64

4,462.57

195,382.35

7

195,382.35

732.68

280.69

5,195.25

195,101.66

8

195,101.66

731.63

3,281.74

5,926.88

191,819.92

9

191,819.92

719.32

294.05

6,646.21

191,525.87

10

191,525.87

718.22

295.15

7,364.43

191,230.72

11

191,230.72

717.12

296.26

8,081.55

190,934.47

12

190,934.47

716.00

3,297.37

8,797.55

187,637.10

Such a large extra payment is typically not within reach of
the average homeowner. For illustrative purposes, the amount allocated to extra
payments is not entirely important so long as it’s comparable between methods.
Comparing the two methods, making an extra payment per month
yields a slightly larger reduction in principal than the periodic lump sum
payments.
This is so because of the principle of compounding interest.
Even though the difference is relatively slight for the first year, because the
loan is allowed to compound on the interest that, under the lump sum scheme,
has not been paid for that month as compared to the monthly payment scheme, the
slight effect of such compounding adds up over time.
While it yields a difference of $51.52 per year (perhaps a
decent dinner for two), over the course of thirty years, these two payment
plans compare thusly:
Amortization + Extra Payments per year

Total Interest

$60,970.91


Extra Amount per Payment

750.00

Total Payments

$260,970.91

Amortization + Lump Sum Transfers

Total Interest

$61,804.05


Frequency:

4 months

Extra:

$3,000.00

Total Payments

$261,804.05

This scenario assumes that cash is available to make such
extra payments, and even so, the difference is $833.14 in favor of simply
making equivalent monthly payments.
If one assumes that new debt will be issued (such as a
credit card advance, let’s assume at an 8.333% annual interest rate) to cover
the cash payments towards a larger loan, the summary is as follows:
Borrowing
to pay extra

CC Interest

538.25

Mortgage Int.

$61,804.05


Savings:

($1,371.38)

Total Interest

62,342.29

Total Payments

$261,804.05

While this data alone will not summarize or justify every
situation, when considered alone, it is clearly advantageous to stick to a
simpler, steadier, consistent monthly payment plan to pay off the loan as
quickly as possible with minimal outlays towards interest.
The problem with presentations such as the Worth Account,
however, is that they do not compare scenarios like the comparison above.
Instead, they compare their scenario with not making any extra payments at all,
which looks like this:
Base Amortization (No extra Payments)

Total Interest

$164,813.42


Total Payments

$364,813.42


Of course making some
extra payments is always better than making no
extra payments. However, if one is charged even 1% of the supposed savings
between the schemes presented and not doing any extra payments at all, then one
would be convinced that they are saving $102,471. 1% of that would equal
$1,024.71. That expenditure would wipe out the entirety of the savings gained
by simply making equivalent monthly payments without having to pay for the
program.
In essence, the consumer is paying for the program to cost
them even more money.
I think this is a really good article. You make this information interesting and engaging. You give readers a lot to think about and I appreciate that kind of writing.
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