Question

Do not answer using a percent sign, a dollar sign or with a number containing commas. For the questions involving rates, you can answer as a percent (for example 10) or as a decimal (for example 0.1).

1.4

Assume you purchased a share of stock for $80 on January 1, 2008 and sold the share of stock for $30 on December 31, 2012. If the stock paid no dividends what your average yearly growth rate?

1.5

Suppose the average growth rate for a security has been 5% per year for 15 years. You sold the security for $200,000. How much did you pay for the security?

1.6

Assume the average growth rate for a security has been 3% per year for 20 years. You purchased the security for $50,000. At what price did you sell the security?

Answer 1

1.4). Purchase price of Stock on January 1, 2008 = $80

Selling price of Stock on December 31, 2012 = $30

For No of years stock been kept = 4 years

Stock did not paid any dividends

Calculating Average Yearly Growth rate:-

Average Yearly Grwoth rate = (Selling Price/Purchase Price)^(1/n) - 1

where, n= no of years = 4

Average Yearly Growth rate = (30/80)^(1/4) - 1

= -21.75%

1.5)

Average growth rate for a security for 15 years = 5% per year

Security sold for = $200,000

Calculating the Buy Price of Security:-

Buy Price = Sell Price/(1+r)^n

where, r = Average growth rate = 5%

n= no of years = 15

Buy Price = $200,000/(1+0.05)^15

= $200,000/2.07892817941

= $96,203.42

So, the amount pay for the security is $96203.42

1.6)

Average growth rate for a security for 20 years = 3% per year

Security Purchased at = $50,000

Calculating the Sell Price of Security:-

Sell Price = Buy Price*(1+r)^n

where, r = Average growth rate = 3%

n= no of years = 20

Sell Price = $50,000*(1+0.03)^20

= $50,000*1.80611123467

= $90305.56

So, the amount sell the security at $90305.56

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