## The Math Behind the Minimum: Calculating the true cost of credit card minimum payments

Most credit card companies keep their exact algorithms for determining minimum payments under wraps. However, there are whole threads of research by mathematicians and statisticians who try to break down the math behind the minimums, using something called the Bond Evaluation Formula.

Quite simply, it is:

?=?(1+?)+?(1+?)2+…+?(1+?)?=?∑?=1?(1+?)−?

Got it?

If that’s just slightly ahead of your high-school level calculus, we don’t blame you, so today we’ll break down a more straightforward way to calculate the real cost of minimum payments.

In fact, there are several ways your bank and credit card companies may calculate your minimum payments, but they usually range from 1% to 5% of your total balance.

__Some basic facts about average credit card debt and interest rates these days:__

__Some basic facts about average credit card debt and interest rates these days:__

- Average credit debt is approximately $14,718 per household
- There are 156 million total cardholders over 54 million households.
- That adds up to 1.235 trillion individual credit cards!

- The average family has 13 cards if you add up their credit cards, retail charge accounts, gas cards, etc.
- 13.04% average credit card interest rate

Now, let’s look at payoff estimates for that $14,718 debt balance on credit cards at 13.04% Annual Percentage Rate.

__The Big Payoff__

__The Big Payoff__

If you paid only minimum payments every month, it would take approximately 31 years to pay off and $16,772 – in interest alone! That means you’d pay $16,772 in addition to the $14,718 original principal balance, for a total of $31,490!

Another way of thinking of it is that the pair of jeans or household goods you purchased on your credit card for $100 will actually cost you approximately $214 if you just pay the minimum!

Remember, that assumes you make the monthly minimum, but the interest rate stays the same, there are no annual fees, late charges, and you don’t spend another dollar on your cards – which virtually never happens over 31 years!

**In fact**, studies show that even small purchases that we finance or pay for with credit cards add up significantly.

That’s even true for relatively small purchases you may buy without a second thought and put on your card. We’ll assume an interest rate of 18%, and a minimum payment of 2% or at least $15 for small balances.

__Here is how long it would take you to pay these off, with the total true cost to you:__

__Here is how long it would take you to pay these off, with the total true cost to you:__

**iPad**

**Spent:** $399.99

**Minimum Payment:** $15

**Time to pay off:** 35 months

**Interest paid:** $114.66

**True cost:** $514

**Shopping trip **

**Spent** $425

**Minimum Payment:** $15

**Time to pay off:** 38 months

**Interest paid:** $132.57

**True cost:** $557.57

**Apple MacBook Pro laptop**

**Spent:** $1,499.99

**Minimum Payment:** $37.48

**Time to pay off:** 153 months – 12.75 years!

**Interest paid:** $1,671.69

**True cost:** $3,170

**Vacation for the family**

**Spent:** $2,295

**Minimum Payment:** $45.90

**Time to pay off:** 317 months (over 26 years!)

**Interest paid:** $5,281.86

**True cost:** $7,577

__The other drawbacks to paying the minimum may be just as harmful!__

__The other drawbacks to paying the minimum may be just as harmful!__

If you like paying double or even triple (or much more!) what you spent on your card over decades, that’s your business.

But you should be aware that there are other profound negatives to paying only the minimum.

**For instance**, consumers who pay the minimum are more likely to go delinquent on accounts, exceed their limit, and otherwise bungle their debt management, according to a study by the credit bureau TransUnion.

Other new credit scoring models – such as ones by VantageScore – may penalize consumers who pay only the minimum every month, especially when it comes to applying for a mortgage.

Too often, consumers try to remedy their credit card woes by “juggling” their balances with zero-interest introductory offers and balance transfers. Unfortunately, that usually makes the problem worse in short order, as the rates skyrocket once those introductory periods expire, monthly payments go through the roof, and the debt load climbs even higher.

__Calculating the opportunity cost of paying only the minimum:__

__Calculating the opportunity cost of paying only the minimum:__

By far the biggest detriment to paying only the minimums is the opportunity cost. It’s also something that you’ll almost never read about in personal finance blogs or profiles on credit card management.

**For instance**, let’s take a look at our original example of a $14,718 credit card balance at a 12.04% Annual Percentage Rate. In that scenario, it took 31 years – or 372 months – and $16,772 in interest alone to pay back the debt using only minimum payments.

Let’s say that this person paid cash instead. That means they’d have about $300 (the estimated monthly minimum payment) freed up every month instead of paying it to their credit card company every month.

Ask any financial planner what they can do with $300 per month over 31 years, and they’ll start jumping up and down with excitement!

For example, (and this is just a hypothetical for educational purposes), let’s say you somehow managed to pay off your credit card debt (or not pay with cards in the first place) for that $14,718 worth of purchases.

So, you now had **$300** freed up on your budget every month and handed it over to a financial planner or just put it in a mutual fund, etc.

Based on the average 6% rate of return for the S&P 500 stock index (adjusted for inflation), you’d amass a nest egg of $313,593 at the end of those 31 years!

Remember that the other alternative is just using that same money to send in your minimum payment every month to pay off credit cards. So, you wouldn’t just be saving $16,722 (in interest) but missing out on the **OPPORTUNITY** to invest that money and watch it grow – an incredibly powerful swing!

__What else could you do with that $300 monthly?__

__What else could you do with that $300 monthly?__

- Amass an emergency fund
- Accrue six months’ worth of savings
- Pay down your mortgage faster
- Pay off your car loan
- Invest in a business or any other profitable venture

As you can see, the math behind the minimum payments is shocking – and not at all in the consumer’s favor!

__There’s a better way – debt negotiation and settlement!__

__There’s a better way – debt negotiation and settlement!__

If you’re faced with $20,000, $45,000, or even $60,000 in credit cards and other debt but are just paying the minimums (or close), there’s a better way! Contact Roundleaf Inc. for a complimentary analysis to see if you qualify for our debt negotiation and settlement program! A brighter financial future may be within reach!