This week in class we did our Financial Unit in my Grade 11 University math class. The intention was to do lessons on series (the summing of a set of terms that are added or multiplied by a fixed rate over a long period of time). This nicely relates to the concepts of compound interest and savings and borrowing, which I would discuss with my class.

One of the things that I wanted to show my class was that small amounts of savings can make huge impacts on the long term. My first example was the classic where there are three brothers/sisters who begin investing at different times. The first person invests $1000 from age 15-24. The second person invests $2000 from age 25-35. The final person invests $3000 from 35-65. You can guess I think with compound interest who comes out ahead. Depending on the interest rates (shown by me in an Excel spreadsheet), you can show the differences between a 5% or a 10% or a 12% interest rate over 30 years what the change will be.

Another example I gave was the "latte" example. Specifically, if instead of going to Tim Horton's you instead invest this $3 per day at 9% for 34 years (I word it that you are 16 today and you do this until you are 50), how much will you have? The idea is to have the students think how this small spending can affect them in the long run. (For the non-students in the audience, the answer is $247,220.76).

The other question that we like is "If _____ has 37 years until he/she retires, and is able to invest at 7.8% compounded weekly and wants to have $1,000,000 at that time, how much must (s)he save each week? How much of this is interest?". The answers are $88.85 per week savings and $829,052.60 interest earned. I like this example for the class because we can discuss the reality of 7.8% interest over 37 years, and how the small savings make an impact.

My final example I give to the class is on borrowing money. I tell them the main ways to pay back loans are to get lower interest rates, to round their payments up to the nearest $20 or $100, and to make lump sum extra payments that will go directly to the principle. I give examples with all of these to show the effect that it has (I have a neat spreadsheet for it).

The numerical example I give them to demonstrate is this: "_____ purchases a house for $220,000 when (s)he graduates high school. If the interest rate is 5.2% compounded monthly and (s)he can afford a payment of $1000, how many months will it take him/her to pay this loan?". This question generates a lot of ooh and aahs because of the answer and the follow-up. The answer is 709 months (or almost 59 years) for this to happen. The amount of interest charges would be $489,000!!!

My continuation is to ask the class if the monthly payments go up to $1100, how much more quickly the loan will be paid off. The answer is it will now take 466 months (or almost 39 years). Still not that impressive, but by raising your payments $100 per month, you have saved $218,400 in interest (charged $292,600 interest)

Here is the rest of the calculations:

Payment: $1200 - Time: 366 months (30 years) - Interest Charged: $219,200

Payment: $1500 - Time: 233 months (20 years) - Interest Charged: $129,500

Payment: $2355.01 - Time: 120 months (10 years) - Interest Charged: $62,601.20

Obviously I picked these numbers for a reason: for the $1000 payment, initially $953.33 is interest (only $46.66 paid against the loan). Additionally, to show the class that even though $1000 sounds like a lot of money on a loan you have to check the numbers.

One thing that sort of shocked me about the class was that they didn't understand the concepts of savings and borrowing and how it is related to a bank. If they are able to give you a savings account at 2% and then loan your money out to someone else at 5%, that is profit for the bank and how it is done.

Finally, the concept of tradition was still alive in my class. That being if they have banked with Royal Bank all their lives, that they will continue to go to get their mortgage through Royal without doing any comparisons of what is available. I used to have an assignment where the students would go to two "traditional" bank, and then one international and one online bank to compare rates and I will go back to this next year.

## Monday, December 21, 2009

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