Secrets of being a millionaire: investment compounding
July 4th, 2007In most occassions, fortune doesn’t come over a night, a month, or a year. Patience is a good character in investment. If a investment fund is well managed, the fund will increase exponentially instead of linearly.
Although many people may have learned compounding interest, it needs to be well reviewed again.
Suppose a person invested $1,000 in a mutual fund today and the mutual fund has a nice annual return rate of 10%. As of 2008 Jul, 4th, there will be 1,000*(1+10%)=$1,100 in his account.
As of 2009 the same day, the amount in his account will be 1,100*(1+10%)=$1,210. Let’s rewrite the equation to be 1,000*(1+10%)*(1+10%). This equation looks more straight forward. Intuitively, you can see the equation is like: p*(1+r)*(1+r) and p is the principle and r is the return rate. Also you can see, the number of years determines the number of terms of (1+r). If investing 3 years, the equation is p*(1+r)*(1+r)*(1+r).
Since p is always $1,000 in this case, the real factor affect your investment is the terms after p, that is (1+r) to the power of number of years invested, denoted as (1+r)^n. Obviously, the more years of investment, the bigger the (1+r)^n. This is so called compounding!
In fact, people always tend to look at (1+r)^n. For example, in the case above, the r is 0.1, if we invest approximately 8 years, the fund will double($2,000), for another 7 years, the fund will double again ($4,000).
What if you make a yearly investment of $1,000 at a rate of 10% return? The equation will be: p*(1+r)^n+p*(1+r)^(n-1)+…p*(1+r)=p*(1+r)*((1+r)^n-1)/r. In this case, if you invest for 5 years and at the end of the 5th year, you’ll have $6715.6 in your account. If you invest 30 years, you will have $180,943.4, the total you invest is $30,000 and your gain is $150,943.4.
It’s magical, isn’t it? The example is a yearly investment of $1,000. What if you invest $1,000 monthly at a monthly rate of return only 1%? After 30 years, you’ll have $3,529,913.77. Yes, you’ll be far more than a millionaire!