Statistically speaking, consumer debt in the U.S. is short of four trillion dollars as of 2018 and rising at a rate of less than 7%. In Canada, which has one tenth the population of the US and roughly one tenth the US economy, consumer debt is approaching two trillion dollars.

In other words, households are in debt. But, what they don’t get because the traditional financial platitudes and mediocre accounting mindsets are etched into their minds is that debt has two distinct classes — there’s good debt and there’s bad debt. Let’s define each class and then move on to two excellent strategies for debt reduction and elimination.

## Good debt, bad debt

Tradition has bad definitions of good and bad consumer debt. I prefer the following definition, largely motivated by Robert Kiyosaki, but broken down into further categories:

**Good debt:**Money you’ve borrowed that makes you more money. For instance, you cousin lent you $5,000 on 6% interest for a year, and you purchased some investment with 10% return within three months.**Bad debt:**Money you’ve borrowed and sunk in spending. For example, you got a credit card with a $5,000 limit and 19.99% APR and purchased a vacation package for $3,500. Bad debt can be smarter than this:*Smart bad debt:*Money you’ve borrowed at the lowest interest rate*which has the potential*to turn into good debt (e.g. getting a mortgage at the lowest interest rate, but unwittingly realizing the potential that eventually renting the place can make you money.)*Dumb bad debt:*Money you’ve borrowed at some interest rate and spent without making any profit. This is the vacation package example, but also your ordinary situation. Your goal should be to get out of this as soon as possible. Moving forward I’ll refer to ‘dumb bad debt’ simply as ‘bad debt’.

## An example

Let’s take a situation involving bad debt. Suppose you have five debt instruments with the following current balances:

- Credit Card 1: $10,000, APR: 19.99%, min payment: $200
- Credit Card 2: $ 5,000, APR: 12.99%, min payment: $60
- Credit Card 3: $12,500, APR: 15.99%, min payment: $250
- Line of Credit: $18,500, interest: 7.25%, min payment: $370
- Loan from a cousin: $5,500, interest: 6%, no min payments, so we have some “false” breathing room here

Finally, suppose you have done your home budgeting and have come up with $1,000 per month to invest in bad debt elimination.

The total current bad debt amounts to $51,500, which would take a few lives to pay off using just the minimum payment amounts (assuming all else equal in your life — good luck with wealth building). Now, let’s take a look at the two strategies to eliminate the debt above: the practical Robert Kiyosaki “Rich Dad” strategy, and a strategy I’ve successfully used in the past because, well, I like math.

## Strategy one: The practical Kiyosaki approach

The Kiyosakis, in one of their podcasts, recommend the following (summarized) approach to eliminate bad debt:

- Acknowledge the fact you’re in bad debt and make an exhaustive list of all the bad debt you owe, including interests and any other constraints.
- At that point, stop accumulating bad debt.
- Hire a bookkeeper, if you can, to think and act like the rich.
- Determine the order to pay your debts,
**such that you can see results quickly**to feel encouraged to kill more bad debt. This is the crux of the Kiyosaki approach. They recommend starting with the smallest debt, committing to paying it off while you merely allocate the minimum payment amount to the other bigger debt instruments, and then move on to the next smallest debt balance. - Find a way (and not an excuse not) to come up with an extra $100-200 per month (after tax) to allocate to your debt payoff.

Let’s apply this strategy to our example. We begin by paying off credit card 2 currently at $5,000, since it is the smallest balance in the list. We commit to paying only the minimum amounts for the other debt instruments, except for the loan from your cousin, which supposedly gives you a break. From your $1,000 monthly limit, you are left with $1,000-($200+$250+$370) = $180 to allocate to credit card 2. With this scenario, you’ll pay off credit card 2 in three years, with an extra $979.66 in interest.

At the end of credit card 2 payoff, or at month 35, the remaining balances are as follows:

- Credit Card 1: $8,429.51, APR: 19.99%, min payment: $200, interest paid for the first 3 years: $5,569.95 (see amortization schedule from any payoff calculator)
- Credit Card 3: $8,809.95, APR: 15.99%, min payment: $250, interest paid for the first 3 years: $5,177.35
- Line of Credit: $8,468.91, interest: 7.25%, min payment: $370, interest paid for the first 3 years: $2,970.09
- Loan from a cousin: $6,550.59 (=5500x(1+6%)
^{3}), interest: 6%, no min payments, interest compounded for the first 3 years: $1,050.59

Total debt after the payoff of credit card 2 = $32,258.96. Headway!

Next in line is the cousin’s loan — after all it’s compounding and it happens to be your next smallest debt. How much would you allocate to it monthly? Allocate to it whatever you were paying for credit card 2 ($180) plus another $100 (because you will have figured out a way to make an extra $100 per month) = $280 per month, while you continue paying the minimum for the other debt instruments. You will pay off that loan in two years (25 months) with an interest of $433.34. After two years (or 59 months since you started applying this strategy), your bad debt situation is as follows:

- Credit Card 1: $6,510.49, APR: 19.99%, min payment: $200, interest paid for the next 2 years: $3,171.03 (see amortization schedule from any payoff calculator)
- Credit Card 3: $4,721.69, APR: 15.99%, min payment: $250, interest paid for the next 2 years: $2,346.35
- Line of Credit: $0.00 (yay!), interest: 7.25%, min payment: $370, interest paid for the next 2 years: $673.59

Look at that — you’ve killed the line of credit! Five years from where you started with $51,500 in bad debt and the effort you made two years ago to increase you after-tax monthly income by $100, have left you with a total bad debt of $11,232.18.

To gain your freedom from bad debt, you can now take the $370 minimum payment you were making to the line of credit you just killed and the $280 you used to pay off your cousin’s loan, and you start killing the remaining debt instruments with a monthly payment of $650. You continue to pay the minimum for credit card 1 at $200 per month, but allocate $450 to paying off credit card 3.

In 12 months, you will have paid off credit card 3 with an interest of $398.99. The balance on credit card 1 is $4,607.25 and the interest you paid on that card for the last year is $1,091.23.

It’s been six years. Now you can kill your final bad debt balance of $4,607.25 with a monthly payment of $650. It’ll only take you 8 months with a interest of $337.51 paid during that period.

A little less than 7 years later, you are bad-debt free because you didn’t accumulate bad debt, you found a way to make an extra $100/month, and you paid the debt starting with the smallest balance first. The total interest you have paid is equal to $23,766.34.

Even though you are now bad-debt free, could there have been a smarter way to pay off your bad debt by minimizing total interest paid, which turned out to be 45% your initial balance? Let’s look at my strategy next and see if we can answer that question positively.

## Strategy two: The smart-ass interest-minimization approach

*Question:* Given the monthly budget of $1,000 you possess to expense against bad debt, how can you distribute it among your debt instruments so that you minimize the total interest paid once the entire balances have been eliminated?

This is obviously an optimization problem and it requires some thinking to set up. Let’s begin with a generic model:

Suppose you have *n* debt instruments with current balances *A*_{1}, *A*_{2}, …, *A*_{n} each with monthly interest rates *r*_{1}, *r*_{2}, …, *r*_{n}, a monthly limit of $*M*, and monthly minimum payments of *m*_{1}, *m*_{2}, …, *m*_{n}. Suppose you wish to pay monthly amounts *a*_{1}, *a*_{2}, …, *a*_{n} to your debt instruments *A*_{1}, *A*_{2}, …, *A*_{n}, then what should those amounts be such that the total interest paid is minimized in the end?

The resulting objective function, *B*(*A*_{i}, *a*_{i}, *r*_{i}, *t*) for *i* = 1, 2, …, *n* and a number of months *t*, can be expressed as:

Thus, the intent is to pay off the whole balance (i.e. *B* = $0) at some point in time *t*, as early as possible, such that the following constraints are satisfied:

- Σ
_{i}(*a*_{i}) =*M* *a*_{i}≥*m*_{i}*a*_{i}≤ M- Balance
_{i}= Σ_{i}(*A*_{i}(1+*r*_{i})^{t}–*a*_{i}[(1+*r*_{i})^{t+1}– (1+*r*_{i})]/*r*_{i}) ≤ 0 - 0 <
*t*< T, where T could be, say, 60 years

Another way to look at this problem is to maximize the subtrahend by minimizing the time *t* so that the whole balance is paid off.

(*See the derivation of this model toward the end of the article.*)

In our example, we have five debt instruments (*n* = 5), a monthly limit *M* = $1,000, and the following balances, monthly interest rates, and monthly minimum payments:

*A*_{1}= $10,000,*r*_{1}= 19.99%/12 = 1.6658%,*m*_{1}= $200*A*_{2}= $5,000,*r*_{2}= 12.99%/12 = 1.0825%,*m*_{2}= $60*A*_{3}= $12,500,*r*_{3}= 15.99% = 1.3325%,*m*_{3}= $250*A*_{4}= $18,500,*r*_{4}= 7.25% = 0.6042%,*m*_{4}= $370*A*_{5}= $5,500,*r*_{5}= 6% = 0.5%,*m*_{5}= $0

We thus want to have *B* = $0 by finding the optimal monthly payments *a*_{1}, *a*_{2}, *a*_{3}, *a*_{4}, and *a*_{5} and the shortest number of months *t*, such that the following constraints are optimally or heuristically satisfied:

*a*_{1}+*a*_{2}+*a*_{3}+*a*_{4}+*a*_{5}= $1,000*a*_{1}≥ $200*a*_{2}≥ $60*a*_{3}≥ $250*a*_{4}≥ $370*a*_{5}≥ $0*a*_{1}≤ $1,000*a*_{2}≤ $1,000*a*_{3}≤ $1,000*a*_{4}≤ $1,000*a*_{5}≤ $1,000- t ≥ 0
- T < 120 months (assume 10 years, but we'll run the 80 months from the previous strategy as well)
- Add here the five balance constraints (Balance
_{i}≤ $0)

Now, you can use an optimization product, such as MS Excel Solver, to set up the six-dimensional model and get some results. Such optimization problems may be solved with the GRG Nonlinear module, or you can use any evolutionary algorithm (which is slower and takes more time tweaking, but is likely better at finding an optimal solution). The goal of the optimization method will be to provide an allocation of the monthly $1,000 available amount over the five debt instruments, such that all constraints are met (minimum payments, maximum allowed payments, paid off balance zero or less, etc.).

Here’s a screenshot of how I would set it up in Excel:

The area in yellow is the objective function; here’s the formula I typed in C17, based on model *B* above:

` =C6*(1+C11)^C19-C21*(((1+C11)^(C19+1) -(1+C11))/C11) + C7*(1+C12)^C19 - C22*(((1+C12)^(C19+1)-(1+C12))/C12) + C8*(1+C13)^C19 - C23*(((1+C13)^(C19+1) - (1+C13))/C13) + C9*(1+C14)^C19 - C24*(((1+C14)^(C19+1) - (1+C14))/C14) + C10*(1+C15)^C19 - C25*(((1+C15)^(C19+1) - (1+C15))/C15)`

The area in gray is the set of decision variables which the optimizer will play with to arrive at our objective *B* = $0. The values in that area are initially blank — the solver will fill those out.

Finally, the constraints that follow are self-explanatory and discussed above.

Here’s how I added these parameters in the Solver add-in. Note the target value of 0 for the optimization function, and the set of constraints in the list. Regarding the GRG Nonlinear solver options, I selected multi-start and played around with the population numbers and convergence, ultimately sticking with a population 600 and a convergence rate of 0.001:

Running the solver produces the following result:

Due to the hard nature of the optimization problem, you’ll likely get a sub-optimal solution, e.g. one that violates the $1,000 per month constraint, as in our case. We got monthly payment allocations $262.40, $113.50, $302.31, $370.00, and $106.91, for a total sum of $1,155.11. That violates my monthly budget *M* = $1,000 by $155.11. Thus, I need to subtract this value from the individual debt monthly payments as follows: a_1 = $261.40 – 22.72%*$155.11 = $227.17, and so forth with the other four. Once this is done, adjust variable *t*, increasing its value until *B* = $0. This entire process takes no more than five minutes. Here’s the final result:

Notice the final results that this experiment produced: In less than 74 months, I could optimally pay off my bad debt using the listed monthly payments $227.17 for credit card 1, $98.26 for credit card 2, $261.71 for credit card 3, $320.32 for the line of credit, and $92.55 for the cousin’s loan, with add up to my monthly budget of $1,000. The corresponding percentages are 22.72%, 9.83%, 26.17%, 32.03%, and 9.26%.

Now, to align this with the Kiyosaki example where, as of year 3, we have an extra $100 to add monthly, we should distribute the $100 monthly payments to each debt instrument based on the optimal solution percentages shown in column G in the figure above. Thus, as of year three, the new monthly contributions to bad debt payoff are: $249.88 (= 227.17 + $100*22.72%), $108.08, $287.88, $352.35, and $101.81 to each debt instrument as ordered above.

For the first two years (24 months), an amortization calculator would help us compute the total interest paid at the end of the second year, which adds up to $11,334.78 (use the optimal allocations before you add the $100 per month). The balances at the beginning of year 3 can be computed by setting t = 24 months:

If you use the amortization calculator with these balances and the new monthly payments (with the extra $100/month), the total interest paid upon debt payoff at month 74 is $10,146.73.

Therefore, the total interest paid during these 6+ years (74 months) is $11,334.78 + $10,146.73 = $21,481.51, or $2,284.83 less than the interest paid off using the Kiyosaki strategy and a few months earlier as well. Now, for those of you who, like myself, believe that a dime contains a god, this difference is significant. Obviously, it requires the kind of smart and fast thinking that Rich Dad never had, but both methods are fun to experiment with.

**Bottom line:** Get more educated in financial matters. The alternatives are gloomy: you’ll either die poor or you’ll become a Communist and, then, die poor.

## Derivation of *B*(*A*_{i}, *a*_{i}, *r*_{i}, *t*)

Without loss of generality, assume you have only one debt instrument, i.e. *n* = 1. Then,

- at
*T*= 0, balance*B*_{0}=*A*_{1} - at
*T*= 1, subtract payment*a*_{1}from*B*_{0}, and apply interest*r*_{1}on the remaining balance:*B*_{1}= (*A*_{1}–*a*_{1})(1 +*r*_{1}) - at
*T*= 2, subtract payment*a*_{1}from*B*_{1}, and apply interest*r*_{1}on the remaining balance:*B*_{2}= (*B*_{1}–*a*_{1})(1 +*r*_{1}) = [(*A*_{1}–*a*_{1})(1 +*r*_{1}) –*a*_{1}](1 +*r*_{1}) =*A*_{1}(1 +*r*_{1})^{2}–*a*_{1}(1 +*r*_{1})^{2}–*A*_{1}(1 +*r*_{1}) - …
- at
*T*= t, we have (by induction),*B*_{t}=*A*_{1}(1 +*r*_{1})^{t}–*a*_{1}(1 +*r*_{1})^{t}–*a*_{1}(1 +*r*_{1})^{t-1}– … –*a*_{1}(1 +*r*_{1}) =*A*_{1}(1 +*r*_{1})^{t}–*a*_{1}[(1 +*r*_{1})^{t}+ (1 +*r*_{1})^{t-1}+ … + (1 +*r*_{1})]

Now, let *S* = (1 + *r*_{1})^{t} + (1 + *r*_{1})^{t-1} + … + (1 + *r*_{1}).

Multiply both sides by (1 + *r*_{1}):

(1 + *r*_{1})S = (1 + *r*_{1})[(1 + *r*_{1})^{t} + (1 + *r*_{1})^{t-1} + … + (1 + *r*_{1})] = (1 + *r*_{1})^{t+1} + (1 + *r*_{1})^{t} + … + (1 + *r*_{1})^{2}

Subtract the first equation from the second to get:

(1 + *r*_{1})S – S = (1 + *r*_{1})^{t+1} – (1 + *r*_{1}).

Then S = [(1 + *r*_{1})^{t+1} – (1 + *r*_{1})]/*r*_{1}.

Therefore, *B*_{t} = *A*_{1}(1 + *r*_{1})^{t} – *a*_{1}S. **QED**

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*Header photo:* istockphoto.com