As explained in How does Money work – Fractional Reserve Banking legal tender money gets into general circulation mainly through loans. Almost all bank loans created need to be paid back with a certain percentage interest. When you consider that all money in a country is loaned out by a bank and banks want that money paid back along with more money (interest), things begin to get a little complicated. How can people pay back the initial loan amount (principal) and interest? The answer is they can’t, or at least not everyone can; the money supply in a country is lower than the money owed to a bank. This means people need to compete to get their share of this limited supply of money and as with all competitions, there are winners and there are losers. Winners gain profits and make more money and losers in this competition go bankrupt. Interest is basically a fee on the money you borrow. It could be considered like rent on the use of the money that was given to you.
Simple and Compound Interest
Simple interest: interest is paid on only on the original principal:
Simple Interest = Principal x Interest Rate x Term of the loan
= P x i x n
For Example: $100 @ 10% after 10 years = $100 x 0.10 x 10 = $100 of interest
Compound interest (or compounding interest) is interest calculated on the initial principal and also on the accumulated interest of previous periods of a deposit or loan. It is the Total amount of Principal and Interest in future (or Future Value) less Principal amount at present (or Present Value).
= [P (1 + i)n] – P
= P [(1 + i)n – 1]
where P = Principal, i = annual interest rate in percentage terms, and n = number of compounding periods for a year.
Continuing with the above example, what would be the amount of interest if it is charged on a compound basis? In this case, it would be:
- 10% of 100 after year one = $10. This is then added to the original $100 to make $110
- For year two the interest is 10% of $110 = $11. The total principal is now $121.
After 10 years the total interest paid on a $100 loan at 10% annual interest would be $159.37!
See table below for a yearly breakdown:
So, compound interest increases at an exponential rate. Compound interest can be your best friend when it comes to investments; interest compounding over time can be a potent factor in wealth creation. It can also cause loan repayment to become much higher than the initial principal. While simple and compound interest are basic financial concepts, becoming thoroughly familiar with them will help you make better decisions when taking out a loan or making investments, which may save you thousands of dollars over the long term.
Compounding Periods
When calculating compound interest, the number of compounding periods makes a significant difference. Generally, the higher the number of compounding periods, the greater the amount of compound interest. So for every $100 loaned over a certain period, the amount of interest accrued at 10% annually will be lower than interest accrued at 5% semi-annually, which will, in turn, be lower than interest accrued at 2.5% quarterly.
Examples of Power of Compounding Savings:
- The compound annual growth rate (CAGR) is commonly used to calculate returns over periods of time for stock, mutual funds and investment portfolios. It can be used to check fund manager performance etc. For example, if a market index fund has provided total returns of 10% over a five-year period, but a fund manager has only generated annual returns of 9% over the same period, the manager has underperformed the market.
- A modest 3% annual rate of return on $100,000 would grow to $180,611 after 20 years. Whereas an annual return of 6% on the same initial investment ($100,000) would grow to $320,714 after 20 years.
- If the objective is to save $1 million by retirement at age 65, based on a CAGR of 6%, a 25-year old would need to save $6,462 per year to attain this goal. A 40-year old, on the other hand, would need to save $18,227, or almost three times that amount, to attain the same goal.
- The fable in which the ruler of India wanted to reward his palace wise man for inventing the game of chess. The wise man said he would like one grain of rice on the first square of the chess board, double that amount on the second square, on the third square, double the amount on the second and double the number of grains of rice on each of the next 62 squares on the chess board. The ruler thinking it was a modest request, called his servants to bring the rice, the rice soon filled the chess board and then the whole palace. In fact the total number of rice grains would be around: 18,446,744,073,709,551,615. Here’s a detailed breakdown on Wikipedia: Wheat and chessboard problem
- Theodore Johnson, a UPS worker never made more than $14,000 a year but saved 20% of everything he ever earned and retired with more than $70 million, because of the power of compound interest.
- Tony Robbins Book Unshakeable is a great book on how to use compound interest to gain financial freedom: Unshakeable: Your Financial Freedom Playbook
Conclusion
Get compounding working for you in your savings and investments and always make sure you thoroughly understand the cost of loans, credit card debts etc. This will make a huge difference to your long-term net worth.
