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Business - Commission and Interest Rate

by Bon
(Pa)










































The buying and selling commission schedule shown below is from a well-known online discount brokerage house.


Transaction Size Commission Rate
$0-$2,500 $19+ 1.6% of principal
$2,501-$6,000 $44 + 0.6% of principal
$6,001-$22,000 $62 + 0.3% of principal
$22,001-$50,000 $84 + 0.2% of principal
$50,001-$500,000 $134 + 0.1% of principal
$500,001+ $234+ 0.08% of principal

1. Show that the commission on 500 shares at $15 per share is $84.50?

2. Taking into consideration the buying and selling commissions in the schedule find annual rate of interest earned by each investment?

An investor purchases 500 shares at $14.20 a share, holds the stock for 39 weeks, and then sells the stock for $16.84 a share.

Comments for Business - Commission and Interest Rate

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Jul 08, 2013
Commissions and Rate of Return
by: Staff


Answer

Part I

1. Show that the commission on 500 shares at $15 per share is $84.50?

Transaction Size


$15 per share * 500 shares

= $7500



Commission Schedule

$6,001-$22,000 $62 + 0.3% of principal


$62 + $7500 * 0.3%

= $62 + $7500 * 0.003

= $84.50



2. Taking into consideration the buying and selling commissions in the schedule find annual rate of interest earned by each investment?

An investor purchases 500 shares at $14.20 a share, holds the stock for 39 weeks, and then sells the stock for $16.84 a share.

Investment to purchase 500 shares at $14.20 a share


Stock


$14.20 per share * 500 shares

= $7100


Commission


$62 + $7100 * 0.3%

= $62 + $7100 * 0.003

= $83.30


Total Investment = Stock + Commission


$7100 + $83.3

= $7183.30



Return when 500 shares sold at $16.84 a share


Stock


$16.84 per share * 500 shares

= $8420


Commission


$62 + $8420 * 0.3%

= $62 + $8420 * 0.003

= $87.26


Total Return = Stock - Commission


$8420 - $87.26

= $8332.74





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Jul 08, 2013
Commissions and Rate of Return
by: Staff


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Part II

Net Return of purchasing 500 shares at $14.20 per share and selling 500 shares at $16.84 a share


Net Return


$8332.74 - $7183.30

= $1149.44



Periodic Interest Rate over the 39 week holding period


Periodic Interest Rate = (Net Return ÷ Initial Investment) * 100


($1149.44 / $7183.30) * 100

= 16.0015591719683 %



Calculation of Periodic Interest Rate







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Jul 08, 2013
Commissions and Rate of Return
by: Staff


----------------------------------------------------


Part III


Annual Interest Rate


Annual Interest Rate = (Periodic Interest Rate ÷ Fraction of year in holding period)


(16.0015591719683 % / (39 weeks / 52 weeks))

= 21.3 %




Calculation of Annual Interest Rate





Note: this is the simple interest rate (annualized).

To compute the weekly compound interest rate, use the following formula:

Weekly Compound Interest Rate = ((Final Amount Received) / (Initial Investment))^(1/t) – 1

Weekly Compound Interest Rate = ((8332.74) / (7183.30))^(1/39) – 1

Weekly Compound Interest Rate = 0.0038132377604

Weekly Compound Interest Rate = 0.38132377604 %

To compute the annual compound interest rate, use the following formula:


Annual Compound Interest Rate = (1 + Weekly Compound Interest Rate)^52 – 1

Annual Compound Interest Rate = (1 + 0.0038132377604)^52 – 1

Annual Compound Interest Rate = 0.219

Annual Compound Interest Rate = 21.9 %








Thanks for writing.

Staff
www.solving-math-problems.com



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