An investor purchased 150 shares of stock at $15.80 per share. The investor hold

Question

An investor purchased 150 shares of stock at $15.80 per share. The investor holds the stock for 39 weeks and then sells the stock for $19.25 per share. Use the commission schedule to find the annual rate of interest earned.

Cost: 150 * 15.80= $2,370

Commission: $2,370 * 0.016= 37.92 + 25.00= $62.92

Total Investment: 2370 + 62.92= $2,432.92

Cost: 150 * 19.25 = $2,887.50

Commission: $2887.50 * 0.011 = 31.76 + 38 = 69.76

Total Return: 2887.50 - 69.76 = $2817.74

A=P(1+r)^t             A= 2817.74        P= 2432.92            t= (39 weeks / 52 weeks)= 3/4

2817.74=2432.92(1+r)^3/4

Principal Commission Under $2500 $25 + 1.6% of principal $2500 - $7500 $38 + 1.1% of principal Over $7500 $105 + 0.5% of principal

Explanation / Answer

Cost: 150 * 15.80= $2,370

Commission: $2,370 * 0.016= 37.92 + 25.00= $62.92

Total Investment: 2370 + 62.92= $2,432.92

Correctly done

Cost: 150 * 19.25 = $2,887.50

Commission: $2887.50 * 0.011 = 31.76 + 38 = 69.76

Total Return: 2887.50 - 69.76 = $2817.74

But the formula for the Annual interset earned, A=P(1+rt)

so A= 2817.74        P= 2432.92            t= (39 weeks / 52 weeks)= 3/4

2817.74=2432.92(1+r*3/4)

(1+r*3/4)=2817.74/2432.92

(1+r*3/4)=1.15817

r=(1.15817-1)*4/3,

r= .21089= 21.089%

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