# Discounting Notes before Maturity– Math w/ Business Applications, Simple Interest Chapter

Discounting a note before maturity were going to take a look at the concept of discounting a note before we
actually do some calculations. Notes can be bought, and sold just like
anything else that has some tangible value to it so hang on to that thought, and
here we have an illustration of someone perhaps selling a note or discounting a
note. Here the manufacture you manufacture some goods someone buys from you, and you offer them a loan for delay of making payment for the items that they
just bought. So you’re the holder of this note it has value with specific terms,
and so on so several months roll by but prior to the maturity date
you are in need of some cash so you go to a bank, and the bank agrees to buy
this note that you’re holding from the buyer.
They will calculate the value of it give you payment, and now are the note holder that the buyer then will pay when the maturity date arrives. So let’s take
a look at another example in this case we have a simple interest note we have a
value of \$5,000 6% interest for 150 days. What is the maturity value of this well
we need to calculate the cost for the interest by taking principled times
rate times time. We have an interest of \$125 so when this
note matures the holder of the note will receive \$5,125 so what happens if
you bail out early? The term of the note is 150 days but
fifty days into that term you need to receive cash for this note that has a
potencial maturity value of \$5,125. You go to a bank, and
the bank agrees to purchase the loan at a discount rate of 7.5% they will charge
you a fee, and when on note is sold prior to its maturity date the fee
is always discounted so we’re going to calculate the cost or fee for selling
early, and it’s based on the number of days that the bank will hold the note
until it’s due. Because you’re going in only after fifty days, and the
length is 154 maturity we subtract the difference and use the 100 remaining
days to calculate the cost or the fee for selling early. So we take the maturity value at times
the discount rate the bank is offering times the remaining time the time the
bank will hold this loan or note until maturity, and since its discount we
will take the maturity value minus the bank discount to determine the proceeds
of this discounted loan the selling of this note which means you the original
holder of the note will receive \$5,018.23. This procedure works the same regardless of whether the original loan is a simple interest or if it is a
simple discount note. Here we have the specifics of this simple discount note
they’re asking us how much will you get if you keep this note the entire
term, because it’s a discount note the face value is the maturity value so
\$9,000. Whoever this was loaned out to they had less than this they had the
proceeds use of the funds from this interest note. So again if we ask the
question what happens if you bail out early? Say 30 days into the loan, and the term of
this loan, and the note that you’re holding from this loan is 120 days. What happens to the nine thousand dollar
value of this note a bank agrees to purchase the loan at a discount rate
of 6% their fee, and when a note is bailed out early the purchaser always discounts. How it
starts could be simple or discount simple
interest or simple discount but when it sold prior to maturity it will always be
a discounted note so we will take its value times the interest rate given for the
discount times the number of days the bank will hold this note until it matures,
and here we can see on this slide the mature time is 120 days the bail
out early it’s only after 30 days the difference it’s ninety days so to
calculate the bank discount we will take the mature value of 9,000 on this original
simple discount note times it by the discount rate times it buy the remaining
time or the time the bank is going to hold this in terms of a year to find our
discount what will the original holder of the note receive because it’s
discounted we take the maturity minus the bank discount for a value of 8865
dollars. So let’s look at a couple examples of finding the proceeds when we discount a simple interest note very similar to what we just saw, and here’s the details the maker is the
the music group the person holding the note or loaning
the money is Blues recording it’s a two hundred day simple interest owed interest
rate of 12% and it has a face value of \$4,800. So here we have some specifics it
started on March 24th the maturity value was determined by taking the principal
times the rate times the time expressed in a year, and here’s the details for
that arriving at a mature value of \$5,120.
On August 15th the holder of this note the Blues Recording decides that they
need their value out of this note now so they sell it to a bank the bank deducts a fee for the maturity value of the note, and this is always discount
we’re starting out with a simple interest note, when it sold early it
will be discounted. The bank purchasing this note is going to charge an interest
of 12.5 percent over the time that is remaining on this loan so we would need
to do some calculations to determine the number of days here showing is 56 days
so the charge for the fee for purchasing this note that has a mature
value of \$5,120 will be to take that mature value times the discount rate
given by the bank times the time that the bank will hold
the note until it is do which is 56 days expressed as a year so over 360 amounts
to \$99.56 the holder of the note in other words the Blue Recording will
receive the proceeds found by taking maturity value minus the bank discount. In this next example we have Jorge Rivera making a
loan with Dayton Finance hundred fifty days simple interest note with 11
percent interest, and a face value or principle of \$9,200 if they ask us for
the due date, and the start date is March 27th we would add 150 days to the day of
the year march 27th and then translated into it calendar date of august 24th. The
maturity value is found by taking the principal times rate times time in
years, and adding it to the principle which is given here \$9,621.67. If this note is sold early
and a bank agrees to purchase it it will be discounted. The bank is charging a
discount rate of 12% for the remaining days we would need to determine the
difference between April 24th and August 24th which results in 122 days. The bank
discount then is the maturity value times the discount rate times the
remaining time that the bank will hold this note until maturity, and money to a
little over \$391. The holder or in this case the payee Dayton Finance will receive the proceeds but to real value minus the bank discount for
a value of \$9,230.39. We have another example here where it’s simple interest
loan made on july 10th the face value is 2000 the term is 72 days, and the
rate is 11%. As the holder of this note goes through the seventy two day period on August second they sell this note, and the bank agrees to purchase the note at
a discount rate of 12% and they’re asking us a series of five questions. When is the due date we would need to look up July 10th day of the year add 72 to that, and then translate that some into a date
which turns out to be September twentieth. What is the mature value we
can see that this is a simple interest loan with a principle of 2000 so we need to do a calculation of principle times rate times time in years, and add it to
the principal resulting in \$2044 the discount period then is from the discount date when the holder the original holder of the note sells it to the bank, and the
time that then the bank holds it until the maturity date so we need to know the
difference between August 2nd and the due date of September 20th
subtracting those results in 49 days. What is the fee for purchasing this note
before its maturity is discounted using the bank discounts formula which is
maturity value times the discount rate given here we only use this original
rate to calculate the maturity value of the loan discount rate is used for
calculating the fee for selling this note early times the remaining time that
the bank will hold this loan until mature. Which results in \$33.39, and then the
proceeds of this will be the mature value less the fee the bank is charging to take this
loan on before or note before the due date resulting in a proceeds of \$2,010.61.