# Mortgage Math ProblemNovember 9, 2012 8:00 PM   Subscribe

Please teach me how to solve this problem related to a Home Equity Line Of Credit. While I am looking for an answer, I am equally interested in learning the math required to solve the problem.

Assumptions:
- HELOC with interest only payments required.
- Last month's interest = \$88.74.
- Currently paying \$1,000 per month, mostly principal.
- Interest rate is 2.240% when balance is \$50K or greater.
- Interest rate is 2.740% when balance is less than \$50K.
- HELOC balance is now just over \$50K.
- If money is put in savings account, it will only earn 0.150%.
- If payments of \$1,000 per month continue, the next payment will bring the balance below \$50K and thus will raise the interest rate 0.500%.

The question(s):
1. Would it be better to defer the interest rate increase by paying interest only for some period of time and putting the balance of the \$1,000 in the savings account each month, or would it be better to keep paying the \$1,000 per month despite the interest rate increase?

2. If it would be better to defer the additional principal payments, at what point should the savings be used to make a large principal reduction?

posted by The Architect to Work & Money (4 answers total) 2 users marked this as a favorite

I spent a bit of time on this, and I think the answers are:

1) Better to pay interest only for some time.

The short version is that there's an easy way to figure out a lower bound to the number of months - it's the value of the principle for which the interest at 2.74% equals 50,000 at 2.24%. Taking the shortcut of monthly compounding that's about \$38,864 via:

88.74 = x * (2.74% / 12)
X = 88.74 / (2.74% / 12)
X = \$38,864

Between \$50,000 at 2.24% and \$38,864 at 2.74% you'll be paying more in interst each month - if you visualize a graph there's a big jump in interest per month at \$50,000, \$38,864 is where the amount finally goes back below the current value.

So at a minimum you would want to pay the interest only and save your \$1000 at any positive rate of return until you had enough saved up to pay down the loan \$11,100 or so in one go. That's a little more than 12 months at \$912 per month, so that's a lower bound on B.

Now that you have a minimum, should you hold out longer? No. Once you put the \$11,000 in the loan, every \$1000 additional you pay down the loan saves you about \$2.30 in interest per month. The \$11,000 you're holding in the savings account at that point generates about \$1.37 per month. So it doesn't make sense to hold on to the savings account any more, and optimum B = minimum B.

Summary, assuming I'm right - put the money in the savings account until you can lower the principle enough with a lump sum to make the new monthly payment the same as your current monthly payment at the lower rate.

About 12 months. At which point you will have saved yourself a grand total of \$45.
posted by true at 9:27 PM on November 9, 2012 [1 favorite]

true, that seems like a great answer. I couldn't come up with such a straightforward way to visual the solution. Thanks!
posted by The Architect at 10:52 PM on November 9, 2012

You've already got the answer about what to do with your HELOC, but, while your profile doesn't say where you're located, you may want to look into a savings account that can earn more than .15%:
Canada, US, many other places(though you can find higher than what they have listed in the US and Canada, so take with grain of salt).
posted by birdsquared at 12:20 AM on November 10, 2012

birdsquared, thanks for your reply also, you make a good point. The savings account in question is linked to the HELOC so I can make automatic transfers for my monthly payments. Since I will now collect the monthly principal payments for 1-year, I will considered finding a higher yield place to for the additional \$912 per month.
posted by The Architect at 7:26 AM on November 10, 2012

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