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# Mortgage Math Problem

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# Mortgage Math Problem

November 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?

Thanks for your help!

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!

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

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

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

posted by The Architect at 7:26 AM on November 10, 2012

This thread is closed to new comments.

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

anypositive 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]