Submitted by: Submitted by Hailants
Views: 229
Words: 300
Pages: 2
Category: Business and Industry
Date Submitted: 10/17/2012 04:05 AM
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%