###### Wealth Management For Young People

I was very surprised when a graduate student once asked me why we don’t use 0.3 instead of 30%. This lack of understanding reflects some flaws in our educational system. Students are normally taught the concepts of percentage and interest in secondary one or two. However, if teachers in school don’t teach about its applications, student may not know its relevance and subsequently know how to put it into practice. Percentages are extremely useful in daily life such as when calculating a rebate on a nice shirt or knowing how much tip to give the busboy. For this article’s purpose, I will focus on the topic of wealth management and how to save money in the bank using simple or compound interest.

At what age should one begin to learn about wealth management? Most wealth management books indicate that it is best to start when one has their first \$1000. One may not be able to tell a big difference early on. However, statistics have shown that big differences can be seen in 20 years between one with and one without wealth management skills. I once mentioned the topic of wealth management to a highly educated man in his mid-40’s. The response I received from him was quite interesting: he told me he didn’t bother with wealth management because he didn’t have enough money. It was then clear to me that he hadn’t learned about this topic early on. Therefore, all I could do was wish him luck because he was now paying for what he may have disregarded at a young age.

The first concept of interest that one needs to know is the difference between simple interest and compound interest which can be seen clearly in the table below. To simply things, I used \$1000 capital as deposit in the bank and a 10 % bank yearly interest rate to illustrate. Simply for reference, nowadays, the bank yearly interest rate is only about 2 -3 %, but in 1994 the bank interest rate was 13 – 15 % per year.

By using simple interest rate In 5 years, one will receive \$1000 x 10 % (per year) x 5 (years) = \$500 interest.

It means that after 5 years, one will have \$1500 without managing his/her wealth.

Contrarily, by using compound interest rate in 5 years, one will receive a higher interest.

To summarize, the following formula for compound interest can be obtained:

Total amount = capital x ( 1 + 10 % ) n,       n = number of years

In five years, the difference between simple and compound interest is

\$1,610.41 - \$1,500 = \$ 110.41

The difference will be:

1,000 x ( 1 + 10 % ) 20 - [ 1,000 + 1,000 x 10 % x 20 ]

= 1,000 x 1.1 20  - 3,000 = 1,000 x 6.7275 – 3,000

= 6,727.5 – 3,000 = 3,727.5

The power of compound interest, which is the exponent function (taught in secondary five),vs. simple interest, which is the linear function (taught in secondary three), can be seen in the graph below.

The formula of simple interest is the following:

Total amount = 1,000 + 1,000 x 10% x n (years).

By replacing the total amount as variable Y and in n years, n as variable x, one gets a new formula in the form of a linear function:

Y= 100 x+ 1,000

On the other hand, the formula of compound interest is the following:    Total amount = 1,000 x ( 1 + 10 % ) n,    n = number of years. This formula can be seen as an exponential function:

Y= 1,000 x 1.1x

The differences are much more obvious as the years go by, using the same bank 10 % yearly interest rate and deposit of \$1,000 capital in the first year as an example.

In the case discussed above, there is only a deposit of \$1000 in the first year. However if one deposits an additional \$1000 every year, with the same 10 % yearly interest rate, the total amount he/she will receive after 20 years will be substantial. Another way to more easily calculate the growth is using geometric series, a concept taught in secondary five. In the following article I will discuss the same concept by using the golden rule of 72 to calculate one's debt to income ratio and one’s ratio of annual income vs. cost of house to see if he/she can afford to buy a house.

If there is such a difference between simply using simple interest or compound interest, how big do you think the difference is when wealth management skills are used along side?