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?

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

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