Understanding interest

Hundreds of years ago loans were regarded as forms of help that one owed his neighbor in distress. To profit from the distress was considered to be evil and unjust.

The noun usury is from the Latin usura, meaning the "use" of something; borrowed capital for example. Usury was once defined as "where more is asked than is given," and was prohibited by the Church and State. It was considered to be a form of robbery. Collecting interest today is not considered to be robbery, but if the interest is excessive, it is considered to be usury.

It was gradually accepted that a loss could occur through lending - the Latin verb intereo means "to be lost" -interest was a loss, and the word interest gradually came to mean the compensation due to a creditor because of a loss incurred through lending. This loss was considered to be the difference between a lender's current position and that in which he would have stood if he had not made the loan.

In early times, loans were interest free, but incurred the penalty of interest if not repaid promptly. Lenders then saw the light and adopted the practice of charging interest from the beginning of the loan.

Today we have two types of interest:

• simple, or fixed interest - which arises from the principal sum only.
• compound interest - which arises from the principal with the interest added at stated times, as yearly, twice-yearly, etc. Interest on interest.

If one borrows money and agrees to repay it plus 10% interest when the loan is repaid, the principal amount of the loan would be repaid plus the 10%, regardless of the repayment date. This is simple interest -interest on principal (the amount borrowed).

However, if one agreed to repay the loan at 10% interest per annum a loan is immediately created with compound interest, because if the loan is not repaid at the end of the year, the 10% interest due will be added to the indebtedness, and when the loan is repaid at a later date, interest will be paid on the new outstanding balance of the loan, which requires interest to be paid on interest.

Always remember that the more frequent the compounding, the greater the yield to the lender.

If the interest were compounded twice-yearly, or semi-annually, here is how it would look on $1,000 at 10%.

So the lender, receiving his interest at the end of the year, receives a return of 10.25 % on the 10% loan.

If the loan interest were compounded quarter-yearly, here is the result:

The lender receives 10.38% on the 10% loan.

The foregoing illustrations of actual return only apply if the loan interest is repaid once a year.

If the interest were paid at the end of each period, and the lender simply put the money in his pocket, the money in his pocket draws no interest so he would be getting 10% a year regardless of the compounding. For example, if the lender received the interest in two periods, the borrower would pay $50 interest at the end of each six months. The first $50 would not be added to the loan and therefore interest would not be paid on the $50 as in compounding.

On the other hand, if the borrower paid the periodic interest out of a pile he kept in a shoe box, he wouldn't pay any more than 10%, because money in a shoe box earns no interest.

This is basically why compound interest is said to produce an "effective yield."

The lender, to receive his 10.25% on the 10% loan would either receive the interest at the end of the year, or  immediately re-invest the periodic payment of interest on the same terms as the loan on which he received the interest. Only then would he get his 10.25%, and make the compounding effective.

Interest rates (or factors as they are sometimes called) are easy to establish, providing the payments are to be made with the same frequency. To establish the periodic interest rate on a loan in which the interest is compounded monthly, simply divide the annual rate of interest by twelve. If the interest were compounded quarter-yearly, divide the annual rate by four, and so on.

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