The Effect of Accounting Changes on Business in Australia

Question 1 [7 marks]

A bill of exchange with a face value of $100,000 and 90 days to maturity was taken out on 15 May 2009 at simple interest of 8% p.a. If the bill was subsequently sold on 30 June 2009 at a simple interest rate of 7.5% p.a.

a) What was the % p.a. rate of simple interest earned by the seller for the period? (3 Marks)

b) What was the effective interest rate earned by the seller? (4 marks)

Draw appropriate time-line(s) to demonstrate your calculations.

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Start answer Question 1

a)

Sold the Bill

30th June

$99,103.99

Bought the Bill

15th May

$98,065.56

46 Days 44 Days

Face value - $100,000

Calculating Number of Days

* First Date- Selling Date: 06302009 ENT – 06/30/2009

* Second Date – ↓Maturity Date: 05152009 ENT – 05/15/2009

* ↓Comp Days: 46

Days left till Maturity: 90 – 46 = 44 Days

365V

365 + rn

Bought the bill of exchange

365 (100,000) / 365 + 0.08(90)

= $36 500 000 / 372.20

= $98,065.56

Sold the Bill of Exchange after 46 Days

365 (100,000) / 365 + 0.075(44)

= $36 500 000 / 368.30

= $99,103.99

Part 1:

Profit

Selling Price: $99,103.99

Buying Price: $98,065.56

Total Profit: $1,038.43

Part 2:

Simple Interested Earned by the Seller

Selling price – Buying Price / Buying Price * 100 * 365/N

= $99,103.99 - $98,065.56 / $98,065.56 * 100 * 365/N

= $1,038.43 / $98,065.56 * 100 * 365/N

= 1.0589%

= 1.0589 * 365/46

= 8.4023%

b) Effective Rate Earned by the Seller

p = (1 + i) m/p – 1

p = (1.010589)365/46 – 1

p = (1.010589) ^7.934793 – 1

p = 0.087172 * 100

p = 8.7172%