  # 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

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

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

 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 % 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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