Mortgage Problems and Home Loans

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Ian Maurer                             My Tutoring Home Page

                                                                       Mortgage Problems
                                          and How to Avoid Them with your Home Loan


This page was written with two different groups of people in mind. Students of mathematics need to know how mortgages
work, and so do people who are thinking of buying a house, apartment or land.

If you fall into the second category, I should say right away that I'm not a financial adviser. What I aim to do for prospective
property buyers (and also for students) is to provide you with a good understanding of how mortgages work, so that
you know what the bank manager, financial adviser or mortgage broker is talking about. You can then make an informed
decision. The best way to get a feel for how mortgages work is to have a play with a mortgage calculator, varying the
amount borrowed, the interest rate and the term of the loan and observe the effect on the monthly repayment required.

Definitions: Ask people in the street what a mortgage is, and they will all most likely say it is a house loan, unless you
happen to ask your question in a street full of lawyers. In fact, a mortgage is the transfer of the title deed for the property
to the bank which lends the money. The title to the property is held by the bank as security for the loan until the loan has
been repaid. If the loan is not repaid in accordance with the contract, the bank has the right to sell the property,
and will do so in order to recover the outstanding amount of the loan, plus costs. In the worst case scenario, if you paid
too much for the property (through bad luck, bad timing, or misplaced enthusiasm) and the bank sells the property for
much less than you paid, you can end up owing money to the bank and with no house to live in.

In short, the mortgage is the bit the lawyers argue over. We are only interested here in the details of the associated loan.

But first a few more definitions:

Principal: Not the head of your local school, but the amount you wish to borrow - or to be more precise, the amount which
the bank is prepared to lend to you. In the calculations it is referred to as the amount borrowed A.

Term: The period of time for which the loan is made. The loan must be repaid by the end of the term. For our calculations
the Term is split up into N compounding periods (see below).

Interest: The money paid by you for the right to borrow the Principal. This amount is usually quoted as a rate I in units of
percentage per annum (which means year in Latin). Interest comes in two varieties, Simple and Compound.

Simple Interest is not widely used, except as a basis for comparison between different loans. Simple interest is calculated
as a percentage of the original loan amount (the principal A), and is paid directly to the bank as an annual fee for the use of
the amount loaned. The interest is not added to the loan. The principal, together with the final year's interest, must be paid
back to the bank at the conclusion of the loan term.

Compound Interest is calculated at specified times (usually quoted as daily balances or monthly balances, etc.) and
added on to the outstanding loan balance at the end of the compounding period (see below). You therefore end up paying
interest on not only the principal, but also on the interest which has been added in, or compounded. This is similar to what
happens with a savings account, except in that case compounding works in your favour, as you receive interest on the interest
which the bank has previously paid to you. With a loan, compounding works in the favour of the bank.

Periodic Payment: The minimum regular payment P which you must make to the bank (usually one or more payments per
calendar month) over the term of the loan. If the interest rate does not change, then one such payment per month will pay back
the loan and all of the interest by the end of the Term. Depending on the details of your loan, you may be permitted to make
additional payments, or make larger monthly payments, and therefore reduce the time to pay off the loan. Some loan agreements
specify penalties for early repayment, so it is a good idea to check before you sign up.

Compounding Period: The period of time (most often one calendar month) after which the interest accrued over the period
is added into the balance of the loan (often referred to as the rest period, as in monthly rests, for example). In the early months
of a loan, this event can be a little depressing for you the borrower, as the outstanding balance, after being reduced by one or
more payments, suddenly rises back almost to where it started. An even worse scenario may occasionally occur if interest
rates are raised significantly just after you have signed up for the loan. In this case the interest added may exceed the amount
of your monthly payment, and the outstanding loan balance may exceed the original amount borrowed. This situation will not be
allowed to continue, and you can expect a prompt letter from the bank advising you of the new, higher minimum monthly payment
required to service the loan.

With Daily Balances and Monthly Rests, the interest is calculated on a daily basis, and the sum of these daily interest amounts is
added back into the loan balance at the end of the month. Daily Balances work in your favour. If a loan only offers Monthly Balances
and Monthly Rests then the interest is calculated on the maximum account balance for the month, irrespective of when payments were actually made.

How much can I borrow? The amount which you can borrow depends on many factors. You really need to talk to a licensed
financial adviser to get an objective assessment of how much you can realistically borrow and what the risks are. Some of the
things you need to take into account are:

What is your salary?
Is your salary likely to increase regularly over the next few years at least, at a rate greater than inflation?
How likely is it that you will be out of work in the next few years?
What cash savings or other easily saleable assets (such as shares) do you have to act as a buffer in hard times?
Do you have to support anyone other than yourself, now or in the near future? (spouse, children, etc).
How much do you typically spend on clothes, food and other living expenses? What is the minimum you are prepared to spend?
Do you have an existing loan for a car or other expensive items?
Do you have an outstanding balance on one or more credit cards?
How much will insurance for building and contents cost for your proposed dwelling?
How much will council rates cost for your proposed dwelling?
Are you saving for an overseas holiday?
Is the loan interest likely to be fully or partially tax deductible? (Is this a rental property?)
How much money will you have left to meet your loan payments after all of the above?

This is by no means an exhaustive list, but gives you an idea of the sort of things you need to start thinking about if you are
serious about applying for a home loan. In the old days, banks would generally only lend up to an amount which resulted
in a minimum monthly payment of about 25% of your gross salary (before income tax is taken out). They now seem to be
prepared to lend to around double this level, if your lifestyle (or lack of it) allows you to meet the repayments.

Loans come with a bewildering array of options these days, but if you understand the basics thoroughly, then it should be
easier for you to decide whether or not various options are beneficial for you. Remember that many options (such as
lower interest charges for the first year or two) are designed to entice you to sign up with the particular bank which is
offering them. Such a discount is almost always offset by higher charges later. Banks are not charities. They are businesses,
and are in business to make a profit. So if they appear to be offering you a deal that appears to be great for the first year
or two, do yourself a favour and find out the total cost over the whole loan period.

Mortgage Insurance: Usually insisted on by the bank, unless you are rich enough that you don't really need the loan. The
reason they insist on it is that it is for their benefit, not yours. It is generally a once-only payment which covers the lender in
the event that you default on the loan and they are not able to sell the property for enough money to cover the outstanding
loan balance. If you are borrowing less than 80% of what the bank values the property at, then you might not have to pay.

Mortgage Calculator: There are lots of mortgage calculators on the web, on graphics calculators, as well as the more
fully featured ones which are used as part of the loan application process. The maths involved is not all that difficult, but is
tedious if you try to do it with an ordinary calculator.

I have produced a mortgage calculator using a Microsoft Excel spreadsheet to do all of the hard work. All you have to do is
to download the spreadsheet and open it. It contains no macros or other programs (nor any spam, viruses or other crap),
so it should be accepted by your antivirus program without too much complaint. It was saved as an Excel 97 document,
so that it should work OK for Windows 98 to XP and Mac as well. It does however require you to have the Microsoft Excel
program installed on your computer. (It comes as part of the Office Suite). The spreadsheet is protected, but only to stop
you from accidentally erasing the formulas which make it work. You may remove the protection by following the instructions
which appear if you try to enter data into a protected cell. There is no password.

For a detailed explanation of the maths behind mortgage calculations, please go to my page which explains how the
Mortgage Payment Formula is derived. It is a PDF document (590K), so that mathematical formulae should display and
print properly on most computers.

For further information on a real loan application try MyRate.