Transcript LESSON 7 - Al-Madinah International University

LESSON 7
ANNUITIES, SINKING FUNDS
ANDMATHEMATICS OF BUYING
Learning Outcomes

By the end of this lesson, students should be able to:
◦ Calculate the present value of an ordinary annuity
Calculate sinking funds
Know how an invoice looks like.
Calculate single trade discounts and net cost
Calculate series of trade discounts and net cost
Express a series discount as an equivalent single
discount
◦ Find the list price
◦
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Learning Outcome (contd.)
◦ Understand cash discount
◦ Determine the cash discount due dates
◦ Calculate cash discount using ordinary dating
method
◦ Calculate cash discount using post-dated (AS
OF) method
◦ Calculate cash discounts using end-of-month
(EOM) dating method
◦ Calculate cash discount using receipt-of-goods
(ROG) dating method
Present value of an ordinary annuity
The present value of an annuity finds the value of a
lump sum amount that must be deposited today for it
to grow to a desired value at a specific date in the
future.
 Suppose a firm needs RM 250,000 at a specific date in
the future. The firm can achieve that goal either by
making periodic payments into an account for several
years, or depositing lump sum into an account and
letting the funds grows. The lump sum that can be
deposited today is the present value of the annuity
involving the periodic payments.
 There are 2 methods to calculate the present value of
an ordinary annuity

Using formula
where;
1 1  i  
PVA  Paym ent 

i


n
– Present value of an annuity
Payment – the amount paid
i – Interest rate per compounding period
n – number of compounding period
Using present value of an annuity table

The steps involved to find the present value
from an annuity table are as follows:
 Find the period interest rate, i =R/k and the number of
compounding periods, n =kT
 Find the intersection of the interest rate per
compounding period and the number of compounding
periods per year.
 Calculate the Present Value of an Annuity using the
following formula.

PVA = Payment x number from
Present Value of an Annuity table.
Find the interest earned : I = Amount - (n x payment)
Sinking funds
A sinking fund is a fund set up to receive
periodic investments to achieve a specific
future value at a specific future date.
 A sinking fund table is used to determine
the periodic amount to be invested on a
regular basis to accumulate a known, lump
sum future value.
 There are 2 ways of calculating sinking
fund

Using Formula
1. Formula to calculate sinking funds.
where;
2. Formula to calculate Interest.
SF – Sinking Funds
M – Maturity value
SF  M 
i
1  i n
1
I  M  n  payment
i – interest per compounding period
n – number of compounding periods
Using Table
The steps you need to follow are:
 Find the period interest rate and number
of compounding periods per year.
 Find the intersection of the periodic
payment and the number of periods per
year.
 Find the periodic amount to be invested.

SF = M x Number of sinking fund table

Calculate interest earned:
I = M - (n x payment)
Invoice
An invoice is a printed document for
record the transaction between seller and
buyer. For seller, it is a sales invoice, and
for buyers, it is a purchase invoice.
 The invoice identifies the seller and buyer,
describes the items purchased, quantity
purchased, unit list price, discount terms,
and shipping and insurance charges.

Trade discounts and net
cost

Trade discount is a business term used for
slashing off the original selling price (list price)
of an item and not related to early payment,
resulting in net cost or net price.

Formulas to find the trade discounts and net
cost are as follows:
 Trade discount = List price x Trade discount
rate
 Net Cost/Price = List Price – Trade Discount

Cash discounts



Business sellers often grant time to business customers
(example 30 days) to pay for the merchandise
purchased.
Sellers encourage the buyers to pay promptly as they
require the cash for their operations. Therefore, cash
discount is offered by sellers to encourage prompt
payment of bills by customers.
Cash discount is shown in the invoice as part of the
terms of sales. Thus, it is important to understand the
method to calculate cash discounts.
Methods of computing cash
discounts
Ordinary dating method
This method is the most commonly used method for determining
cash discounts. The date and net payment date are counted from
the date of the invoice.
 Cash discounts are generally shown in an invoice such as:
 3/10, n/40 OR 3/10, net 40
 Read as “three ten, net forty”
 First digit is the rate of discount (3%)
 Second digit is number of days allowed to take the discount (10
days)
 n/40, net 40 is the total number of days given to pay the invoice in
full.

Contd….
• Post-dated (AS OF) method
Sometimes an invoice is post-dated to
give the buyer more time to take the cash
discount. This method calculates the
discount period and the net payment date
starting from the given AS OF date. For
example, an invoice dated July 25 AS OF
August 1 will have both cash discount
date and net payment date counted from
August 1.
Contd…
• End-of-month (EOM) dating method
End-of month dating is similar to
proximo dating. It is written as such
5/10 EOM, and 5/10 prox. which means
that the buyer will get 5% cash discount if
payment is made by the 10th of the month
that follows sale.
 If the invoice is dated on 20 March with
terms of 3/10 EOM, then the cash
discount period is up until 10 April.

Receipt-of-goods (ROG)
dating method
The discount period and the net payment period begin
when delivery is made.
 Abbreviated as ROG, this dating method gives the
buyer time to receive and inspect the goods to ensure
the merchandise received was in good condition.
 The method also allowed the buyer to benefit from a
cash discount.
 An invoice with terms of 6/15 ROG, means 6% cash
discount is given if the invoice is paid within 15 days
from the receipt of goods.

Lesson Summary
The topic explains the basis for annuity
payments and its calculation.
 There are a few cases where may be
involved in annuity payments in life.
 Students should be familiar with way of
computing annuity in order to
accumulates money for some personal
reasons in the future.

Contd..

Similarly, students have learnt the
knowledge involving trade and cash
discounts that usually accompanies buying
and selling of goods between business to
business buyers. Students are reminded to
use the number of each day of the year
table to facilitate calculation for discounts
when offered.