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Loans - Understanding Amortization Print E-mail
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Personal Finance - Mortgage
Written by Omie Ismail   
Thursday, 10 September 2009 15:09

A byproduct of getting a finance degree is that you vastly improve your personal finance abilities.   Loans are just a financial instrument with certain terms associated with them.  Loans are a financial instrument that a bank or investor ("Lender") makes to a borrower.  Typically there is some use of the funds that the Lender approves.  For instance a home mortgage is an "asset backed" loan, which means that if the borrower doesn't pay back the loan, the lender can seize the asset.

Lenders also make non-asset backed loans which require the legal process to recover funds if the borrower defaults on payment.  In general an asset backed loan will have a lower interest rate than the non-asset backed loan for the very reason that they have a piece of collateral that they can recover.  In addition, if the asset is worth something, most borrowers will do anything they can not to default so they won't lose the asset.

So lets say that you have a $100,000 mortgage, a 6% interest rate, and its for 30 years, how much is it going to cost you each and every month?  $599.55.  How did I get that number?  Well I used the PMT function in Excel.  You can use Excel or you can use a payment wizard on the Internet, but its really important that you understand how you get to this number not just automatically calculate it and move on.


Lets first understand conceptually how we get to our $599.55.  Our interest rate is 6% which means that if we only paid interest on our loan we would have $6,000 in interest each year or $500 a month.  But our lender wants all of his money back after 30 years in nice even payments and if we paid him $500, after 30 years we would still owe him $100,000.  This is an interest only loan and is similar to a Home Equity Line of Credit in its initial 10 year period.  Since our lender wants even payments we could take our $500 interest and add to it the $100,000 divided by the 360 months of the loan which would add $277.78 for a total of $777.78.  The banker would be very happy with this arrangement because it fails to account that after your first payment, you have lowered the principal and therefore your interest should be less than $500.

It turns out that $599.55 is the exact amount that you can pay between our $500 interest only and our $777.78 obvious overpayment that over 30 years will exactly reduce our balance to zero.  The term for this is "fully amortizing" and its the most common type of loan.

There are hybrids between interest only and fully amortizing.  For intance, you might get a loan that has a balloon payment at the end of the term.  Common might be a loan that amortizes like a 30 year loan but has a balloon payment for the balance at 15 years.

Lastly, we have assumed that our lender is giving us a fixed rate loan.  In many cases, the lender may instead be offering a variable rate loan which is typically tied to an index plus a certain fixed margin.  For intance, Prime Rate plus 1%.  You may be able to get a lower rate on these loans but you have the risk that the payments will increase if the rate increases.

Its very important to understand what type of loan you are getting and what the terms are.  One of the major problems that occured during the recent housing bubble, is people had no idea what type of loan they were getting and what were the terms associated with it.




So lets take the conceptual view first.  I am borrowing $100,000 and I have to pay it back over 30 years or 360 months.  If we didn't have any interest the the monthly payment would be $100,000 / 36 = $277.78 per month.  Think of that, if the bank were willing to charge you no interest you could go out and buy a $500,000 house for a mere $277.78*5 = $1,389!  Now you can understand why interest rates have such a massive effect on the price of a house.  If you wondered how those people were affording a $500K house, many of them actually could, for about 2 years.  With your six percent mortgage you would have to pay $3,000 a month for that house.  Take it up to 12% and that $500K house will cost you over $5100 a month.  So the first point is that for longer term loans, monthly payments are very sensitive to interest rate changes.   Your monthly payment is going to change alot.


Now there is something else very important going on that you might not see at first glance.  Ideally you want the balance of your loan dropping as fast as possible.  I know what you are saying, "Hey they are both going to be paid off in 30 years, doesn't my loan balance go down at the same rate".  No, it doesn't.  Not only is the interest rate lower, but the balance goes down faster.  If you have a mortgage, this means that you are gaining equity faster.  Lets take our zero percent example again on a $100,000 loan.  After 1 year, you will owe exactly $100,000 less, 12*$277.78 = $3333.33 which is exactly 1/30th of the loan balance.  At 6%, you will have only paid $1,228.01.  So you have built up over $2,000 more in equity at zero percent.


So what's going on here.  When you have a 6% mortgage on $100,000, you are going to pay $6,000/12 in interest in your first payment which is $500.  Remember we said your payment was $599.55, that extra $99.55 is your principal payment.  So the next month the interest will be based on $99,900.45 which will be slightly lower and mean you are paying about $100.05 in principal.  So your principal continues to go down a little more each time then it did the previous month because the balance is less.  Again, the lower the interest, the faster you pay down your loan which will build more equity for you.


Well we don't live in a world of zero percent interest loans but lets take the example of a $500,000 loan at 4.5% (the low that you could have gotten in 2009) and 7.0% (what you might be charged if you don't have your credit or income in order).  On a 30 year loan, the two payments are $2,533.43 and $3,326.51 - ouch!  But that's not the whole story,  lets compare the Equity built up assuming no appreciation of the home.



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