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Author Topic: Math help, please.  (Read 548 times)

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oogyda

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Math help, please.
« on: July 15, 2015, 10:01:59 AM »
I'm hoping some of you wonderful people can help me with a math problem.  I want to figure out what my "effective" interest rate is, if possible. 

Specifically, I pay more toward my mortgage every month than what is required.  Oogydh has noticed that mortgage rates are still declining and has suggested we refinance again.  We have a good rate and I know that by paying more every month, we are "effectively" paying a lower rate.  Or, more precisely, we will have paid a lower rate by the time we pay it off. 

Since there are costs involved with refinancing, I'd like to be able to show him that we can "effectively" match or better that rate. 

Help.
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GreenHall

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Re: Math help, please.
« Reply #1 on: July 15, 2015, 10:09:33 AM »
One of the pre-fab Excel sheets is a amortization schedule. 
I copy paste the same one with different rates, to convince myself that I really am getting something for the extra money each month.

You could do a second sheet with the potential new rate, including costs etc.

(And I can't find spell check to see if I spelled amortization correctly...)

MrTango

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Re: Math help, please.
« Reply #2 on: July 15, 2015, 10:39:16 AM »
By paying more than the standard P&I Payment each month, you aren't lowering your rate.  Interest is still accruing at (X/12)% of the unpaid balance each month.  (X is your annual interest rate).

What you're doing is reducing the principal on which that interest is accumulating and effectively shortening the term of the loan (because it'll get paid off sooner).  This can save you a lot of money over the term of a mortgage loan.

What I would do in your position is use an Excel spreadsheet to calculate the amount of interest you're going to end up paying and how quickly you're going to pay off the existing loan.  I'd actually do this twice: once with just the standard payments and again taking the additional payments into account.  That way, you can see how much money you're saving by paying extra each month.

Then, I'd research the offers that are available to you and use the spreadsheet to determine how much you'll save (if anything) given the fees to close the new loan and the new rate.

DavidH

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Re: Math help, please.
« Reply #3 on: July 15, 2015, 11:03:04 AM »
Your interest rate isn't changing by paying more each month.  What you are doing is reducing the principle on which the interest is calculated, so that you pay less in interest over the life of the loan. 

As an example let's say that you borrowed $100,000 at 4.5% for 30 years; your payment would be $506 per month.  If you are pay an additional $100 per month for a total of $606 you will pay it off 7 years early, but your interest rate remains at 4.5% and your required payment remains at $506 per month for the life of the loan.

If you refinance to a lower rate, say 3.5% per month, your required payment will go down to $449.  If you continue to pay a total of $606 per month, you are now making an extra payment of $157 per month.  This means you will pay it off 11 years earlier. 

shhh its me

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Re: Math help, please.
« Reply #4 on: July 15, 2015, 11:30:23 AM »
    This will give you the tables http://www.webmath.com/index1.html  click "A loan" under the personal finance heading.  Figuring out the total interest at different points paid may help .
Here is a effective rate calculator ...http://www.calculatorsoup.com/calculators/financial/effective-interest-rate-calculator.php .
Here is the formula with explanations http://www.wikihow.com/Calculate-Effective-Interest-Rate.   
This one is for APR which adds in the costs of the loan.http://www.calculatorsoup.com/calculators/financial/apr-calculator.php

Your basic premiss  may be a little off , you're right that you are lowering the amount of interest paid by making more then the minimum payment but if you continue to make the same payment amounts and lower the rate  you will be paying even less interest. You're right that there is a point when you are so far into the loan that neither refinanceing to a lower rate or the rate change is so small it doesn't make sense.





shhh its me

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Re: Math help, please.
« Reply #5 on: July 15, 2015, 11:48:10 AM »
   I think the examples may help........

A $100,000 loan at 4% over 30 years = 360 payments of $477 and total interest of $71,000.  Paying $550 instead = 278 payments and $53,000 paid in interest. A $100,000 at 3% over 30 years is payments of 421 for 360 payments with a total  paid $151,000 and interest paid of $51,700.  So yes if you only compare the interest paid paying more saves almost the same amount  over the life of the loan as paying a lower rate.   Now that doesn't account for inflation $550 today will buy you more then $421 will in 23 years.  OR how it will lower the interest paid if you keep the payment amount the same. But, it also doesn't include closing costs.

oogyda

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Re: Math help, please.
« Reply #6 on: July 15, 2015, 01:03:34 PM »
    This will give you the tables http://www.webmath.com/index1.html  click "A loan" under the personal finance heading.  Figuring out the total interest at different points paid may help .
Here is a effective rate calculator ...http://www.calculatorsoup.com/calculators/financial/effective-interest-rate-calculator.php .
Here is the formula with explanations http://www.wikihow.com/Calculate-Effective-Interest-Rate.   
This one is for APR which adds in the costs of the loan.http://www.calculatorsoup.com/calculators/financial/apr-calculator.php

Your basic premiss  may be a little off , you're right that you are lowering the amount of interest paid by making more then the minimum payment but if you continue to make the same payment amounts and lower the rate  you will be paying even less interest. You're right that there is a point when you are so far into the loan that neither refinanceing to a lower rate or the rate change is so small it doesn't make sense.

Thank you for those references.  I think I'll be able to get what I need out of at least one of those. 
« Last Edit: July 15, 2015, 01:05:57 PM by oogyda »
It's not what we gather along the way that matters.  It's what we scatter.