# ON MONEY: Understanding the Mysteries of Compound Interest | Characteristics

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

Interest can be thought of as the rental fee that the owner of capital charges the tenant (think of the borrower) for using that capital for business and personal purposes. 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 waived 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 potential returns on other investments or uses of those funds that you might have used.

Interest is not the cost of money; it is rather 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 option for reinvestment.

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

In Jill’s example, the first year’s charge for using the capital is the same $80, but the difference is that from the second year onwards, the $80 is added to the capital and the rate of 8% interest is charged on $1,080. , not $1,000. This continuous or compound reinvestment takes place every year for the life of the loan, and after five years, Jill will owe me $1,469.33.

Albert Einstein once said that compound interest was the most powerful force in the universe, and it’s easy to see why. In our Jack and Jill example, 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 saved credit card companies billions of dollars, mainly due to the financial ignorance of card users.

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

So, as we can see from these examples, the number of compounding periods can have a huge impact on the overall cost of the loan. In the case of daily compounding, the effective annual interest rate I charged Jill in the 10-year example was not 8%, but rather 8.79%. Interestingly, in calculating the annual effective interest rates, the underlying calculations assume that the compounding frequency is once per 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%.

You can no doubt see from these simple examples that the topic you are interested in can get very complicated.

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