Very interesting...

FOR most people, financial math is as fascinating and desirable as a 12-hour road trip across the Prairies in a car with a broken air-conditioner on a hot summer day. Both are necessary evils we sometimes must endure to reach a goal, whether a holiday destination or saving for retirement.

But unlike the road trip, financial number-crunching is often an unavoidable aspect of life -- not a vacation choice.

Thankfully, few people ever have to wade into the confusing world of finance much farther than understanding interest rates. But comprehending these rates isn't always as simple as it seems.

At its most basic, interest is expressed as an annual percentage charge on a borrowed amount, or if you're investing, it is a percentage of the sum you lent, paid as a premium for the inconvenience of being out that money for a period of time.

But the way you borrow (or lend) will affect the interest rate you pay (or receive) and how the interest is calculated.

The most obvious number you want to pay attention to is the rate itself. If you're the borrower, you want a lower rate. If you're the lender, you want a higher rate.

Elementary, yes?

The problem is as either borrower or lender of modest means, you don't set the terms. You're likely only going to get as good a rate as the market allows.

In large part, the market for interest rates is set by the Bank of Canada, University of Manitoba economist Fletcher Baragar says.

At the moment, the bank's rate is the lowest it's ever been, and its governor, Mark Carney, has made it clear the rate will stay around 25 basis points (0.25 per cent) at least until next spring. This is good news if you're borrowing money.

"That means, in principle, that all the other rates that banks post as prime rates and mortgage rates are expected to be more or less constant over the next year," says Baragar, associate head of the department of economics at U of M.

The Bank of Canada rate may be the trendsetter -- a suggested rate at which banks would lend to each other -- but the prime rate is always about two percentage points above the bank's rate, and most consumers never get that when borrowing.

Usually, consumers are offered prime plus one or two per cent as the lowest rate. When interest rates are low like they are today, this "bargain rate" often includes mortgage rates too, which typically are the lowest available to consumers because a home is great collateral if a borrower defaults.

But when the prime rate is high, like it was two summers ago at 6.25 per cent, some consumers might have been offered mortgage rates that were below prime -- such as prime minus one per cent.

"People with good credit ratings and good collateral could often negotiate with banks or other financial institutions to get something below prime," Baragar says. "However, that's almost impossible to do today."

These days, even getting the lowest rate above prime isn't as easy as it might have been in the last few years.

"What banks and other financial institutions are doing is they might say, 'Well, the prime rate is not going to change but in terms of who might qualify for the prime rate, or the collateral that you might need to qualify for the prime rate, those criteria are becoming more difficult,' " Baragar says.

Consumers looking to get a loan at the lowest rate available might want to look at what the online financial institutions have to offer as competition, says David Stangeland, an accounting and finance professor at the U of M.

"Check the online institutions like ING Direct because often they'll quote you a lower rate than what the regular banks will quote," says Stangeland, also the associate dean at the Asper School of Business. "What you can usually do then is go back to your bank and say, 'I really want my car loan through you because I do all my business here, but I've been quoted this lower rate.' And more likely than not, your bank will match it."

While conditions are rather good for borrowers, the scenario is reversed if you're lending money to corporations, government or banks. Government bonds and GICs may offer stability in an uncertain economic environment, but these investments pay next to nothing at the moment. Even corporate bonds that carry higher coupon rates (annual interest payments) yield much lower payments because they cost more to purchase than their original value -- not to mention they can also come with a higher risk of default.

Yet, interest-bearing investments -- even paying below the prime rate -- are not bad options for the short term. The inflation rate, which under normal circumstances eats into returns, has remained slightly below or above zero per cent in recent months.

But the interest rate itself isn't the only concern for money-conscious consumers. Interest costs are compounded differently depending on the loan or investment.

The frequency at which the interest charges are compounded affects how much you receive as payment if you invest in a fixed income security, or how much you pay if you borrow.

"The more something is compounded, the higher the effective interest charges are compared to the quoted rate you are shown," Stangeland says.

The rate you are shown annually is often referred to as the APR or annual percentage rate.

The rate that includes the compounding costs is the EAR, the effective annual rate.

It's this rate that represents the real interest costs associated with the debt you carry or the payment you receive for having lent the money.

For instance, mortgage interest is compounded semi-annually, even though your payments are monthly. A five per cent APR amounts to an EAR of 5.06 per cent. On a line of credit, interest is compounded monthly so the EAR is slightly higher.

"If you had 12 per cent per year compounded monthly, the effective annual rate works out to about 12.6825 per cent - or something around there," Stangeland says.

The upside right now, with rates being so low, is consumers don't need to pay much attention to how often interest on debt or investments is compounded. Over the course of the year, a rate compounded monthly at three per cent doesn't amount to much more than one compounded semi-annually -- if at all if the principle amount is less than $10,000.

But as rates go up, which they inevitably will do, the EAR also increases. On small loans, this fractional increase of just a few basis points is still negligible. But for people looking at borrowing amounts larger than $10,000, the slightly higher cost of borrowing can start to add up. It still may be just a few dollars, but isn't it better when those dollars are fattening your wallet rather than somebody else's?

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Simple versus compound

SIMPLE interest charges are rare in the financial world, but some GICs do pay simple interest. What this means is if you invest $100 at two per cent paid annually, you will have $102 at the end of the year. The following year, you will earn another two per cent on the $100 and have $104 in the account. Simple interest charges only apply to the original principal amount, and it's the cheapest way to carry debt (that is, if you can find a lender offering it). If you're an investor, it is likely the worst way to be paid interest.

Most loans charge and many investments, like bonds, pay compound interest. When you make a loan payment, any interest costs that haven't been entirely paid off by the payment are added to the total debt. The next time the interest is calculated, it is done based on that higher debt amount.

Over a short period of time, compound interest and simple interest costs do not differ much, but with longer amortizations, compound interest costs add up dramatically - a bad situation if you're borrowing and not completely servicing interest costs along the way. If you're lending the money, it's ideal.

Typically, though, most consumers make payments amounting to more than just the interest costs so the principal amount is not increasing in value. But when interest costs are compounded more frequently (monthly instead of annually), you can end up being charged interest on interest, which slightly raises the actual interest rate you pay over the course of the year, U of M finance professor David Stangeland says.

"Even if you pay off your line of credit at the end of the month, you'd be charged more interest if the rate was five per cent per year compounded monthly (instead of compounding annually) because in pretty well in every case the financial institution converts the rates to an effective daily rate when doing the interest calculations," he says. "So, the five-per-cent-per-year rate compounded monthly converts into a higher daily rate than a five-per-cent-per-year rate compounded annually. So, it still matters even for only a month."

Here's a comparison of interest costs on two $10,000 loans, both with APRs (annual percentage rate) of five per cent. One is compounded monthly while the other is compounded semi-annually. (Effective annual rates rounded to the nearest hundredth.)

Monthly compounding

Effective annual rate: 5.12 per cent

Interest cost after one year: $511.62

Interest cost after three years: $1,614.72

Interest cost after 10 years: $6,470.09

Semi-annual compounding

Effective annual rate: 5.06 per cent

Interest cost after one year: $ 506.25

Interest cost after three years: $ 1,596.93

Interest cost after 10 years: $ 6,386.16

Here's a comparison of loans for the same amount with an eight per cent APR. Note how the spread between the loan compounded monthly and the loan compounded semi-annually is larger than in the first example.

Monthly compounding

Effective annual rate: 8.30 per cent

Interest cost after one year: $830

Interest cost after three years: $2,702.37

Interest cost after 10 years: $12,196.40

Semi-annual compounding

Effective annual rate: 8.16 per cent

Interest cost after one year: $816

Interest cost after three years: $ 2,653.19

Interest cost after 10 years: $11,911.23

-- www.1728.com Software Systems

Republished from the Winnipeg Free Press print edition September 6, 2009 C6