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Use the commission schedule from Company B shown in the table to find the annual rate...

Use the commission schedule from Company B shown in the table to find the annual rate of interest earned on the investment. (Note: commisions are rounded to the nearest cent.)

Principal (Value of Stock)	Commission
Under $3,000	$32plus+1.8% of principal
$3,000 - $10,000	$56plus+1.% of principal
Over $10,000	$106plus+0.5% of principal

An investor purchases 328 shares at $36.66 a share, holds the stock for 271 days, and then sells the stock for $52.27 a share. Assume a 360-day year.

What is the rate of annual %? Round to nearest three decimal place.

Expert Solution

Step 1: Calculate Total Value of Initial Investment

The total value of initial investment is calculated as below:

Total Value of Initial Investment = Total Purchase Value + Commission on Purchase

where, Total Purchase Value = 328*36.66 = $12,024.48 and Commission on Purchase = 106 + .5%*12,024.48 = $166.1224

Using these values in the above formula, we get,

Total Value of Initial Investment = 12,024.48 + 166.1224 = $12,190.6024

_____

Step 2: Calculate Net Proceeds Realized from Sale of Investment

The value of net proceeds realized from sale of investment is determined as follows:

Net Proceeds Realized from Sale of Investment = Total Sales Value - Commission on Sale

where, Total Sales Value = 328*52.27 = $17,144.56 and Commission on Sale = 106 + .5%*17,144.56 = $191.7228

Net Proceeds Realized from Sale of Investment = 17,144.56 - 191.7228 = $16,952.8372

_____

Step 3: Calculate Rate of Annual Interest

The rate of annual interest can be derived with the use of equation given below:

Net Proceeds Realized from Sale of Investment = Total Value of Initial Investment*(1+Annual Rate of Interest*271/360)

Substituting values in the above formula, we get,

16,952.8372 = 12,190.6024*(1+Annual Rate of Interest*271/360)

Solving further, we get,

16,952.8372/12,190.6024 = 1+Annual Rate of Interest*271/360

1.39065 = 1 + Annual Rate of Interest*271/360

Annual Rate of Interest = (1.39065 - 1)*360/271 = 51.894% (answer)

jeff jeffy answered 2 years ago

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