III – Interest

The Basics

The concept of interest should be relatively straightforward: it is simply the cost of borrowing money.

So for example, if you borrow $200,000 from a bank at an annual interest rate of 5% to be repaid at the end of 3 years, you may be inclined to calculate the interest as $30,000, calculated as follows:

$200,000 loan x 5% interest/year x 3 years = $30,000

In this example, you would repay $230,000 at the end of 3 years – the original $200,000 loan plus $30,000 in interest.

Actually, this is incorrect: the actual interest you would have to pay is $31,525! Therefore, you would actually have to pay to the bank $231,525 ($31,525 in interest plus the $200,000 loan).

What accounts for this difference? The first method of calculating interest is called the simple method. Banks and other lending institutions never calculate interest in this manner. Rather, they will calculate interest using the compounding method. Here is the calculation using this method:

Year 1: $200,000 loan x 5% interest = $10,000

     Add $10,000 interest to original $200,000 loan = $210,000

Year 2: $210,000 loan balance x 5% interest = $10,500

    Add $10,500 interest to beginning $210,000 balance = $220,500

Year 3: $220,500 loan balance x 5% interest = $11,025

    Add $11,025 interest to beginning $220,500 balance = $231,525

As you can see, you borrowed $200,000 at 5% per year for 3 years, and you had to repay $231,525. Therefore, your cost of borrowing was $31,525. We can summarize this in the following table:

Beginning Interest Cost
Ending
Balance (beginning balance x 5%) Balance
 $ 200,000  $   10,000  $210,000
 $ 210,000  $   10,500  $220,500
 $ 220,500  $   11,025  $231,525
 $   31,525

It is extremely important that you understand the distinction between simple interest and compound interest. With reference to our example: in the former, interest was calculated every year only on the amount borrowed. In the latter, interest was calculated on the amount borrowed and interest calculated in the previous year.

You should now start to see that the cost of borrowing can end up being much higher than you were initially led to believe.

Opening Your Eyes

Now let’s extend our previous of example of calculating compound interest. Again, here are the facts:

Amount borrowed: $200,000 in January 2011

Interest rate: 5% per year

Length borrowed: 3 years, to be repaid end of December 2014

However, instead of calculating interest annually, the bank will calculate interest each month during the 3 year borrowing period. It will do this by multiplying the beginning loan balance by 0.4166% each month (5% divided by 12 months = 0.4166%).

For clarity: the annual interest rate is still 5%, but the interest will be calculated every month instead of every year. Here is the result in the following table:

Beginning Interest Cost
Ending
Month Balance (beginning balance x 0.4166%)
Balance
Jan-11  $ 200,000  $       833  $200,833
Feb-11  $ 200,833  $       837  $201,670
Mar-11  $ 201,670  $       840  $202,510
Apr-11  $ 202,510  $       844  $203,354
May-11  $ 203,354  $       847  $204,202
Jun-11  $ 204,202  $       851  $205,052
Jul-11  $ 205,052  $       854  $205,907
Aug-11  $ 205,907  $       858  $206,765
Sep-11  $ 206,765  $       862  $207,626
Oct-11  $ 207,626  $       865  $208,491
Nov-11  $ 208,491  $       869  $209,360
Dec-11  $ 209,360  $       872  $210,232
Jan-12  $ 210,232  $       876  $211,108
Feb-12  $ 211,108  $       880  $211,988
Mar-12  $ 211,988  $       883  $212,871
Apr-12  $ 212,871  $       887  $213,758
May-12  $ 213,758  $       891  $214,649
Jun-12  $ 214,649  $       894  $215,543
Jul-12  $ 215,543  $       898  $216,441
Aug-12  $ 216,441  $       902  $217,343
Sep-12  $ 217,343  $       906  $218,249
Oct-12  $ 218,249  $       909  $219,158
Nov-12  $ 219,158  $       913  $220,071
Dec-12  $ 220,071  $       917  $220,988
Jan-13  $ 220,988  $       921  $221,909
Feb-13  $ 221,909  $       925  $222,834
Mar-13  $ 222,834  $       928  $223,762
Apr-13  $ 223,762  $       932  $224,694
May-13  $ 224,694  $       936  $225,631
Jun-13  $ 225,631  $       940  $226,571
Jul-13  $ 226,571  $       944  $227,515
Aug-13  $ 227,515  $       948  $228,463
Sep-13  $ 228,463  $       952  $229,415
Oct-13  $ 229,415  $       956  $230,371
Nov-13  $ 230,371  $       960  $231,331
Dec-13  $ 231,331  $       964  $232,294
 $   32,294

As you may recall, when interest was calculated annually, the interest payable over 3 years was $31,525. But when interest is calculated monthly, the interest payable over 3 years is $32,294.

What accounts for this difference? Answer: the frequency in which interest is calculated during the borrowing period. Given an annual interest rate, the more frequently interest is calculated (or “compounded”) over the borrowing period, the higher the actual interest that has to be paid. Here’s a summary of what we’ve calculated so far:

Amount “Nominal” Compounding Actual “Real”
Borrowed Rate Method Frequency Interest Rate
 $200,000 5% Simple N/A  $30,000 5.00%
 $200,000 5% Compounding Annually  $31,525 5.25%
 $200,000 5% Compounding Monthly  $32,294 5.38%

As you can see, given: (1) a loan amount; and (2) a quoted annual interest rate (also referred to as the “nominal” interest rate), the actual interest you would pay on the loan will be a function of:

  • The method of calculating interest (i.e., simple versus compounding); and
  • The frequency of compounding during the loan period

So, as you can see from the table above, the “real” annual interest  rate is often higher than the “nominal” (i.e., quoted) annual interest rate you see in advertisements for:

  • credit cards – interest in compounded daily
  • car loans – interest is compounded monthly
  • mortgages – interest is compounded monthly

Takeaway

  • Never finance anything with a credit card. Annual (i.e., nominal) interest rates for credit cards can be as high as 30% and the interest on outstanding balances is compounded daily, so the real interest rate you’re paying can be astronomical.
  • Since interest on mortgages are compounded monthly, pay down your mortgage as quickly as you can. Compounding works both ways – the slower you pay down your mortgage, the more interest you end up paying whereas the more quickly you pay off your mortgage, the less interest you end up paying. Most banks will allow you to prepay 15 to 25 percent of the original mortgage balance once a year during the term of your mortgage.

© Copyright Fong and Partners Inc., 2011.

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