1. Interesting Interest

by M. Bourne

Disclaimer

This discussion is simplified. Interest rates are changing all the time - check your local banks for latest rates.

This site does not give investment advice.

Banks need money to make money. How do they get money in the first place? They borrow it from us, the customers.

They pay us, of course, but not very much at all. What they pay us is called interest.

Let's say we want to lend a bank $1000 for a 12 month period. We can either deposit the money in an ordinary account (bad idea) or get a term deposit (still not good, but better.)

The rates for 12-month term deposits in early 2011 were:

USA `1.4%` p.a.  
Singapore `0.5%` p.a.  
Australia `6.0%` p.a.  
Japan `0.1%` p.a. (yep, they pay almost nothing!)
UK `3.0%` p.a.  
Canada `3.7%` p.a.  
Mexico `2.0%` p.a.  

(p.a. stands for per annum, which is Latin for "per year".)

Now, if you want to be paid the full amount of interest, you can't touch that money for 12 months. (You can usually get it out early, but they give you almost nothing. They have had the use of the money but don't give you much of the profit.)

So what does it mean?

Let's take the case where the interest rate is `3%`. Now `3%` of `$1000` is `$30`. So your `$1000` deposit has grown to `$1030` in one year.

Time - and the Power of Compounding

In all this stuff, time is very important. Let's assume we don't touch the deposit for 10 years. Let's see how much we have at the end of that time.

  Amount of Interest Year-end
Amount
Year 1 `3% × 1000.00 = $30.00` `$1030.00`
Year 2 `3% × 1030.00 = $30.90` `$1060.90`
Year 3 `3% × 1060.90 = $31.83` `$1092.73`
Year 4 `3% × 1092.73 = $32.78` `$1125.51`
... ... ...
Year 10 `3% × $1304.78` `= $39.14` `$1343.92`

Our $1000 has grown, but not by much - around 34.4% in 10 years. This growth is very important for growing your money. The power of compounding is a key concept in Money Math.

The Math Behind the Interest

We don't have to do a table when calculating compound interest amounts. Your scientific calculator can probably do it directly for you.

Alternatively, we can use a simple formula to calculate the total amount of money at a particular time, given a certain interest rate.

`A = P(1 + r)^t`

where:

A = amount in the future

P = amount paid at the beginning (principle)

r = interest rate per year

t = number of years

So for our $1000 deposit at 3% pa, the amount we will have is:

4 years: `A = 1000(1 + 0.03)^4= $1125.51`

10 years: `A = 1000(1 + 0.03)^10= $1343.92`

Quarterly and Monthly Payments

Sometimes, banks pay interest quarterly (every 3 months) and sometimes monthly. We need to tweak our formula for such cases.

`A=P(1+r/n)^(nt)`

where

n = number of payments per year

If our (not very generous) bank pays interest quarterly, then `n = 4`.

So if we give them our `$1000` for `10` years and the interest rate is `3%` `p.a., paid quarterly, the amount we get is:

`A=1000(1+0.03/4)^(4xx10)=$1348.35`

It is worth about `$5` more to us than if our payments are yearly - not much, but at least we can go to Starbucks and celebrate.

Higher Returns means More Money

You can see that 3% per annum does not leave us much better off. But there are millions of people around the world who have their savings in low-interest term deposits. And they are effectively giving money to the banks!

Let's see what the amount would be if we could earn more interest. If we can get `7%` per year, then:

`$1000` for `10` years at `7% =$1967.15`

Our money has almost doubled if we get `7%` per year.

How about `10%` per year?

`$1000` for `10` years at `10% =$2593.74`

This is better still - our money is now worth almost `2.6` times the amount that we put in.

So how do you get higher returns like this? Mostly, it means putting your money into higher risk investments (shares, unit trusts, property and the like). With a long time horizon, and a mix of different investments, there is a reasonable chance of `7%` return after tax.

Financial Lessons From All This

  • Tom (see the chapter intro) should learn as much as he can about interest and understand the power of compounding.
  • Tom should learn as much as he can about investing - and start doing it - while he is still young.

Money Maths Lesson Plan Suggestions - Interest

  1. Simulate a scenario where students have $10000 to invest. They need to find the best rates. Allow them to choose between a passbook savings account, term deposits, debentures and bonds. What are the risks? What are the returns?
  2. Get students to design a deposit board game, so the players will learn about the power of compounding

Footnotes

  1. Inflation is an important consideration. If you are earning `3%` and if inflation is also running at `3%`, it means you are not making any money at all, in real terms. Your buying power has remained the same.
  2. Tax is another important consideration. Always include tax in any real calculations
  3. When we are calculating money, we usually round off to 2 decimal places because bank accounts usually indicate amounts in cents. Ever wondered what happens to those amounts after the second decimal place? Does it matter? The banks just keep those amounts. With millions of transactions going on each day, these small bits can amount to a lot of money. For most of us, it won't make much difference in a lifetime, but it is good to be aware of how the banks can keep what is really yours.

Rule of 72

In that 7% example above, we saw that the money almost doubled over 10 years. See an interesting shortcut for estimating compound interest amounts in the next section:

Rule of 72.

Also, you can see more on

Exponential Functions.

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