Interest-ing Finance A certain dictionary I use defines interest as 'A sum charged for borrowed money.' Having given the subject this exhaustive treatment, it moves on to other matters. Well, after all, it is not the province of the dictionary to teach finance, so here is what they call in the boardroom a 'broad brush' treatment of the subject for those of you who want to approach your financial education gradually. The amount of interest a borrower pays depends on a number of things: - The amount borrowed (Principal) - The term, or time in months or years taken to repay the loan - The number and frequency of payments - The interest rate, also known as the Annual Percentage Rate or APR. - The method used to calculate the interest The simplest form of interest is called, as you might suspect, Simple Interest. Most types of loans use some variation of simple interest. Compound interest pertains more to deposit accounts, and will not be considered here. The easiest loan to calculate is one which is paid back in a single payment at the end of a year. If the amount borrowed is $ 1000 and the APR is 10%, for example, the amount of interest due at the end of the year is $ 100, and the total due is $1100. Another type is called a Discounted Loan. The lender calculates the interest and deducts it from the principal. In other words the borrower receives the face amount less the interest. The payments are calculated by dividing the total, interest + principal, by the number of payment periods. Here is an example of the calculation: The principal is $5000 and the annual interest rate is stated as 10%. Ten percent of $5000 is $500. $5000 minus $500 is $4500 which is the amount received by the borrower, who pays $500 for the use of it. 500 divided by 4500 is 11.1% The interest rate is already above the stated rate. If the loan is paid back during the year in more than one payment, the actual rate, as compared to the stated rate, goes higher. Because part of the money was used less than a full year. Another form of loan, calculates the interest and adds it to the principal. This is now the face amount on which the interest is calculated. This is called, for obvious reasons, Add-On interest. Suppose you want to borrow $ 5000 at 10%. The lender calculates 10% of $ 5000, which is $ 500, and adds the 500 to the 5000, equalling $ 5,500. This is the new face value of the loan on which the interest is calculated. Taking 10% of $ 5,500 we get $ 550, the interest charged. You get $ 5000 and for this you pay $ 550. Divide it out and it comes to 11% if paid off at the end of a year in one payment. If paid before the end of a year, or paid in installments, the actual interest rate is higher. * * * When the Discounted or Add-On type of loan is repaid in monthly installments, some lenders will rebate part of the interest if the loan is paid off early. The method most frequently used to determine the amount is called the Rule of 78's. There is a program on this disk named Rule78 which figures the percentage of the interest money to rebate, determined by the month in which the payoff is made. The percentage of the rebate is calculated as follows: The sum of the digits from 1 to the number of payments remaining, divided by the sum of the digits from 1 to total number of payments specified in the loan documents. $ 1000 is borrowed for one year at 10% interest, and is to be repaid in 12 monthly payments. If the loan is paid off after the 6th payment.... 12 - 6 = 6 (number of payments remaining) (1+2+3+4+5+6) = 21 (1=2=3=4=5=6=7=8=9=10=11=12) = 78 21 divided by 78 = 26.92% Total interest for full term would be $100 (10 percent of 1000) Rule78 calculates that 26.92 percent of the interest charge should be rebated if payoff occurs after sixth payment is made. Rebate of Interest if loan is paid off after 6th payment would be 26.92 percent of $100, or $26.92 * * * The most common type of loan is one where the repayment is done in equal monthly installments, in which each monthly payment includes one month's interest on the balance remaining unpaid. This is called a Declining Balance or Amortized loan. It is the kind of loan you probably have on your car or mortgage. The amortized loan is the hardest to calculate. For example, you borrow five thousand dollars to buy a used car, and have three years to pay it back. Your first payment must contain enough money to pay the interest on the entire principal for a month, plus an additional amount to pay back part of the principal. Subsequent payments consist of interest for one month on the unpaid balance, plus payment of part of the principal. With each succeeding payment the interest portion will be less than it was the previous month and the amount paid toward the principal will be more, because the unpaid balance is less each time. Yet the total of each monthly payment, interest plus principal, must be the same as it was the first month. Over the course of the loan It must all work out very neatly so that, at the end of 3 years, the loan has been paid off in equal monthly payments. Can it really be possible to figure out a way to do this? Fortunately for people like you and me, a formula was devised years ago, and here it is, as used by most banks to this day: Monthly Payment = PV x (I/(1-(1+I)))^ -N PV (Present Value) - Is the amount of money borrowed. I - Is the monthly interest rate as a decimal. (The annual rate divided by 1200, i.e., by 100 to change it from a percent to a decimal, and by 12 to change it from from yearly to monthly.) N - Is the number of months for which the money is borrowed. ^-N means raised to the power of -N Do not try to work this out in your head. You may end up with a sprained brain. A few of you may be able to figure the monthly payment on your loan with a calculator using this formula. However, since you own a personal computer, there are many good programs available which figure out the monthly payment, and make a printout by month showing interest per payment, principal per payment, balance to maturity, and amount due if the loan is fully paid before maturity. (That which the banks and car dealers call the Payoff.) One such program, HIFI, is included with the CAR BS program. This last, the Payoff, is simply the amount borrowed minus the total of the principal paid to date. If you plan to pay off ANY loan before maturity, it is best to call the bank before you write the check, and ask for the amount due, as there may be other charges involved. From the discussion of amortized loans you may have been able to infer that most of the interest is paid early in the life of the loan when the principal is largest. This makes it hardly worth while, for example, to pay off a six year loan in year five when the remaining interest may be negligible. A final word on the amortized loan equation. You may sometimes see it in a more complicated form than shown here. You will find that the longer equation accommodates a Balloon Payment. Some lenders make the last payment larger than the others, thus name. The object is to make the monthly payments lower. The balloon payment is usually a large one, and the optimistic borrower assumes it will be easier to pay in the future than in the present. This type of thinking is occasionally seen today in certain types of home mortgages where payments start out small and get larger as time passes. * * * If you are still with me, let me congratulate you. You now know enough about loans and interest to be dangerous. End