Simple Discount - Basics
In the Simple discount situation, there is an amount of money (future
value) due on a certain future date, usually within a year; the debtor can
ask for paying in advance and, if the creditor agrees with him, the money to
be paid today (present value) is less than the due capital; in fact the
future value is subtracted by the discount calculated in proportion
to time and rate of discount
The creditor receives the proceeds (present value) of the
loan today
Finding the present value or discounting, as it is commonly called, is not
simply the reverse of finding the
future value by the interest formula
A simple discount rate, r, is applied to the final amount
FV
and results in the formula
where,
D = simple discount on an amount FV
r = simple discount rate
(in percentage)
t = period of time (in years)
Seemingly the formulae of Interest and Simple Discount
look similar; but there is a substantial difference: the amount on which
the formula is applied, is the initial capital in the interest formula whereas
the corresponding amount is the
final capital in the discount formula.
The present value to be paid in advance by the
borrower, can be expressed as a difference between the Future Value and the
Simple Discount
substituting D with the formula, we have
therefore
and finally, collecting FV
The term (100 - rt) is called the discount factor under
simple discount
English version
| Time expressed in years
PV = FV - D
|
D: discount after t years.
FV: future
value, the amount that should be paid on the original maturity date
r: annual discount rate in percentage (%)
PV: present value, is the discounted amount to pay in
advance of the original maturity date
|
Italian version
| Time expressed in years
Vc = C - Sc
|
Sc: discount after t years (sconto
commerciale)
C: future
value, the amount that should be paid at the original maturity date (capitale)
r: annual discount rate in percentage (%) Vc: present value,
is the discounted amount to pay in advance of the original maturity date (valore
attuale commerciale) |
Simple Discount - Period of time is a fraction of the year
The Simple Discount formula applies to short-term investments (less
than a year).
| Time expressed in months
 English
Italian
PV = FV - D
 English
 Italian
|
D:
discount before m
months.
the amount that should be paid on the original maturity date
r: annual discount rate in percentage (%)
PV: present value, is the discounted amount to pay in
advance of the original maturity date |
| Time is expressed in days according to the calendar year
we
are referring to exact simple discount and the fraction of the year
is based on 365 days
 English
Italian
PV = FV - D
 English
 Italian
|
ANNO CIVILE
D:
discount before d days.
FV: future
value, the amount that should be paid on the original maturity date
r: annual discount rate in percentage (%)
PV: present value, is the discounted amount to pay in
advance of the original maturity date |
| Time is expressed in days according to the commercial
year
we
are referring to ordinary simple discount and the fraction of the year
is based on 360 days
 English
Italian
PV = FV - D
 English
Italian
|
ANNO COMMERCIALE
D: discount before d days.
FV: future
value, the amount that should be paid on the original maturity date
r: annual discount rate in percentage (%)
PV: present value, is the discounted amount to pay in
advance of the original maturity date |
Example 1:
Michelle invested a certain amount of money in a bank; at the maturity date she
will receive 5,000.00. Applying the discount rate of 4.8%, what amount would
she get asking to be paid in advance of 3 months?
Answer :
FV = 5,000.00
r = 4.8%
m = 3
D = (FV Ś r Śm)/1,200
D = ( 5,000.00 x 4.8 x 3)/1,200 = 60.00
PV = FV - D = 5,000.00 - 60.00
Hence, Michelle would get 4,940 3 months earlier.
Example 2.
Jeff O'Sullivan has sold goods to a customer for 350 that are due on 30 April. If
Mr O'Sullivan grants an advance payment by the
customer on 15 March using a discount rate of 2.5%, what amount would he get? Use
the direct formula and a 365 day year
Answer:
FV = 350.00
r = 2.5%
d = 46
PV = [FV Ś (36,500 - r x d)]/36,500
PV = [350.00 Ś (36,500 - 2.5 x 46)]/36,500
Hence, Mr O'Sullivan will have 348,90 46 days beforehand.
Calculating the Number of Days of a Loan or Investment
Steps for determining the Number of Days of a Loan are the same of those
used in case of Simple Interest: (see Simple
Interest chapter)
Inverse Formulae
| |
the unknown |
| TIME |
Future Value |
rate of discount |
time |
| years |
 |
 |
 |
| months |
 |
 |
 |
| days/365 |
 |
 |
 |
| days/360 |
 |
 |
 |
Inverse Formula of FV from PV:
| |
year |
months |
days/365 |
days/360 |
| Future Value |
 |
 |
 |
 |
GLOSSARY
Simple discount
|
English
|
Italian
|
Notes
|
| due |
dovuto,
scaduto |
riferito
a un capitale |
| in advance |
in
anticipo |
|
| proceeds |
incasso |
|
| reverse |
contrario,
opposto |
|
| should be paid |
dovrebbe
essere pagato |
|
| rate of discount |
tasso
di sconto |
e.g.:
5% per year |
| grant |
concedere |
|
| customer |
cliente |
|
| simple discount |
sconto
commerciale |
|
| whence |
da
cui |
|
| calendar year |
anno
civile |
365
days per year |
| commercial year |
anno
commerciale |
360
days per year |
| unknown |
incognita |
|
| beforehand |
in
anticipo |
|
| e.g. |
per
esempio |
dal
latino exempli gratia |
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