LESSON 7

1. LESSON 7 ANNUITIES, SINKING FUNDS ANDMATHEMATICS OF BUYING

2. 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

3. 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

4. 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

5. Using formula

6. 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)

7. 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

8. Using Formula

9. 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)

10. 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.

11. 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

12. 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.

13. 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.

14. 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.

15. 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.

16. 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.

17. 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.

18. 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.