Compound Interest has the ability to multiply money almost magically. There is a story that Einstein was once asked, "What is the most powerful force in the universe?" his immediate response was "Compound Interest".
Calculating Compound Interest manually is a bit difficult and in times past tables were used to get a close approximation. The reason it is so difficult to calculate compound interest is that it is not a single calculation but a series of calculations and the numbers change with each calculation.
Here is how it works: Suppose you want to calculate the result of compound interest over a ten year period. For simplicity sake we will say that the interest rate is 10% and that we start with $100. And to keep it really simple, we will specify that the interest is only calculated (compounded) once per year.
At the end of the first year you would have $100 x 10% or $110. So far the interest calculations are simple but as we compound it we find that end of the second year we have $110 x 10% or $11 interest added to our $110 giving us a compounded $121.
Here is a table for the results of the interest compounding for all the years of our compounding period.
Sample Compound Interest Calculations
Value at Year end
Another interesting point in our Calculations of Compound Interest is that during the 5th year the interest earned is actually 14.641 we have dropped the 1 from the calculations because there is no such thing as a tenth of a cent but if we were dealing with larger numbers that fraction may be significant in the future interest calculations. This is another reason that calculating compound interest can be complex. So actually after the fifth year our manual calculations of compound interest are actually no longer entirely accurate.
You will also notice that at the end of the 7th year compound interest has almost doubled our initial investment. The "Rule of 72" tells us that at 10% interest the actual point where compounding would double our money for us is after 7.2 years. After 10 years we have over two and a half times our money and as the time period extends the money grows faster and faster. This is the magic of compound interest.
But as you can see even in this extremely simplified calculation with only ten years (periods) the calculations begin getting difficult (if you don't round) because each compounding period gives you an additional decimal place to keep track of. So without a calculator it becomes extremely time consuming to get an accurate result. It also becomes almost impossible to calculate higher compounding periods like quarterly, monthly, daily and even infinite compounding.
On the face of it it would seem that higher levels of compounding would give us more interest but in actuality they only make minor differences. The major difference comes from the length of time (number of years of the investment not length of the compounding period) and the other major factor is the interest rate. Even infinite compounding only gives a minor boost to the total rate of return.
With all that said here is a calculator you can use to calculate Compound Interest. Note that the Compound Interest calculator has sample numbers of $10,000, 10% and 10 years. Very similar to the numbers I chose for the above example . Note that due to rounding the annual numbers calculated by my manual method are slightly different than the annual numbers presented in the chart by the calculator. My result for compound interest was $259.39 while using the calculator would have resulted in $259.37 but the compound interest calculator was also able to simultaneously come up with a result for Quarterly, Monthly and Daily compounding.