Saving comes in many different forms. Some may invest a lump sum in a savings account at the bank, others may invest monthly in a retirement annuity. It really doesn’t matter how you save, as long as you are saving on a regular basis. Whether you are in a high-income category or a low-income category, you should invest a portion of your income for your retirement or any strategic goal. In this article I will discuss the importance of understanding the technical aspects of saving.
The
principle of compound interest is viewed by some as the best invention since
sliced bread. Compound interest is, in
its purest form, earning interest on interest.
For example, if you invest $100 in a savings account for 3 years at 10% annual
interest, you will earn $10 in the first year, $11 in the second year, and
$12.10 in the third year. See the table
below:
|
Year |
Compounding |
Interest
Earned |
|
1 |
100 x (1+0.1) = 110.00 |
$10 |
|
2 |
110 x (1+0.1) = 121.00 |
$11 |
|
3 |
121 x (1+0.1) = 133.10 |
$12.10 |
|
Total |
|
$33.10 |
The formula to calculate the future value of a lump sum, is:
Where i is the interest rate per period and
where n is the number of periods. It is clear that when you save, your savings
will grow exponentially. It should grow
at the factor of n. The following chart shows the value over time
of a $100 lump sum investment over 20 years:
The above example shows
the value of investing a lump sum with compound interest. Once you have decided on your savings goal,
you can decide to invest a certain amount every month. This is called an annuity. For example, if you invest $100 at the
beginning of every year for 20 years, your investment should be after 20 years:
The formula to
calculate the future value of an annuity due is as follow:
Where i is the interest rate per period and n is the number of periods. The above chart also shows the exponential
growth of your investment due to compound interest. Even if you invest a small amount every
month, it will grow bigger and bigger as time goes by. Please note that we can also calculate the present value of an annuity (like a loan agreement), where periodic payments
are made to pay a loan. This loan amortization
will be discussed in a future article.
It is clear: the
more you save, the more you will have in the future. You should, however, always consider the
interest rate and applicable investment fees before you invest. You should invest your savings where your net
return is the highest. Another important
consideration is deciding on a hurdle rate, or a minimum rate of return. The current inflation rate should be the
absolute minimum required rate. Inflation
eats away the value of money, so your money should grow at least at the inflation
rate, in order to just keep its purchasing power.
Most central
banks use inflation targeting as their monetary policy regime. It is important, under inflation targeting,
to always maintain a positive real interest rate. The real interest rate is simply the nominal
interest rate minus the current inflation rate.
The same principle should apply with your investment: your real return
should be positive.
The message is
clear, start evaluating your financial position and find ways to start
saving. It could be a once of lump sum
or an annuity. You should always strive
to earn a positive real interest rate.
Once you have adapted the savings habit, it should be easy for you to
set goals and start saving towards them.
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