




                              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


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