Mortgage Math Problem

November 9, 2012 8:00 PM

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?

Thanks for your help!

posted by The Architect to Work & Money (4 answers total)

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

1) Better to pay interest only for some time.
2) About 12 months.

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]

Response by poster: 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

Response by poster: 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