Compound interest

ON MONEY: Understanding the Mysteries of Compound Interest | Characteristics

One of the financial topics that is least understood by an alarming number of Americans is interest, and in particular compound interest. In this and next week’s column, we’ll look at interest: both simple and compound, and explain all of the various descriptions of how interest is calculated.

Interest can be thought of as the rental fee that the owner of the capital charges a tenant (think of a borrower) for the use of that capital in business and personal affairs. When you open a savings account at a bank, you are actually lending that money to the bank and the interest the bank pays you reflects the fact that you have foregone the use of those funds while they are on deposit. , and in return the bank pays you interest. The loss of use of funds is often referred to as lost opportunity costs or the potential return on other investments or uses of those funds that you may have used.

Interest is not the cost of money; rather, it is the cost of credit. The money you lend to another person includes the principal, and that person has the use of that principal on credit. Simple interest is the rate paid for the use of capital without any reinvestment option.

As an example, suppose I lend Jack and Jill $ 1,000 each which will be paid back to me after five years. I charge Jack 8% simple interest and Jill 8% compound interest. In Jack’s case, the interest charge is $ 80 each year. I earn this charge every year, and at the end of the fifth year, Jack pays me back the loan principal plus interest charges of $ 400, for a total of $ 1,400.

In Jill’s example, the first year charge for using the principal is the same at $ 80, but the difference is that starting in the second year, the $ 80 is added to the principal and the rate of 8% interest is charged on $ 1,080. , not $ 1,000. This ongoing reinvestment or capitalization occurs each year during the term of the loan, and after five years, Jill will owe me $ 1,469.33.

Albert Einstein once said that compound interest is the most powerful force in the universe, and it’s easy to see why. In our example of Jack and Jill, if the loan had been for 10 years, Jack would have paid $ 800 in interest charges, while Jill’s charges would have totaled $ 1,158.92, more than the original principal. This dialing feature is what has made credit card companies billions of dollars in earnings mainly due to financial ignorance on the part of card users.

In our example, the compounding took place once a year, but suppose I decide to slip into Jill’s loan agreement a statement that the interest will be compounded daily, even though the loan interest rate remains at 8. %. In such an example, Jill would owe $ 1,323.09 in interest charges at the end of the ten years.

So, as we can see from these examples, the number of funding periods can have a huge impact on the overall cost of the loan. In the case of daily compounding, the annual effective interest rate that I charged Jill in the 10-year example was not 8%, but rather 8.79%. Interestingly, in calculating annual effective interest rates, the underlying calculations assume that the compounding frequency is once a year. To illustrate this point, in the first example where I charged Jack 8% simple interest over five years, the annual effective rate was only 6.99%, not 8%.

No doubt you can see from these simple examples that the topic of interest can get very complicated.