Saving interest by rolling credit card debt into a mortgage sounds like a great idea, but does it really make cents?

I use the following scenario: A couple has a house worth $215,000, owes only $200,000 but has $15,000 in credit card debt at 19.99%. They are going to refinance the mortgage to get a 3.5% rate but does it make sense for them to take out the $15,000 in home equity to pay off the cards?
30 years is a long time
Over the life of a 30 year mortgage the borrowers will pay $123,311 in interest for a $200,000 mortgage or $132,559 for a $215,000 - saving over $9,000 in interest.
Extending the term
Paying a lower interest rate doesn't save money when you are paying more interest over a longer period of time. While $15,000 on a 19.99% credit card will take 15 years to pay off it will only cost $2,500 more in interest than rolling it into a 30 year mortgage at 3.5%.

Extending the length of the loan is like driving slower to work: You still burn about the same amount of gasoline and get frustrated because it's taking forever!

You are diluting home equity
By rolling $15,000 in credit card debt into the refi, you will pay $6,500 more in interest and still be behind $9,400 in home equity after 15 years.
Amortization vs Minimum Payments
Mortgages: Every traditional fixed-rate mortgage will require the same monthly payment (principal and interest portion only). When you pay down the balance, the amount of interest generated for the next month is less.

For example: If your monthly mortgage payment (not including taxes and insurance) on a $200,000 mortgage is $900.00 and $315 goes towards the principal then you end up paying the rest, $585, to interest. However, the interest that is calculated for the next month is on the newly-reduced balance of $199,685 ($200,000 - $315 = $199,685). So the interest portion of the next month's payment is reduced by $1 to $584 and the principal portion is now $1 more ($316).

Credit Cards: Minimum payments are based on a percentage of the balance. The minimum payment for a $15,000 credit card will be $600. Pay it down to $5,000 and the bank will only ask for a minimum payment of $200. You are more likely to only send the minimum - and stay in debt longer - when you aren't on a debt elimination plan.

The pain: Paying only the minimum payment on a $15,000 card at 19.99% will take over 15 years to pay off. That's pain, not a plan.
A better option
If you were willing to pay $65 more each month for a $215,000 mortgage payment, why not stick with the $200,000 refi and apply the $65 to the credit cards every month? This will cause the credit card to be paid off 11 years sooner and save $6,600 in interest.

 
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