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Calculating the Desired Parameters

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1. Investments in the stock market have increased at an average compound rate of about 5% since 1905. It is now 2012.

a. If you invested $1,000 in the stock market in 1905, how much would that investment be worth today?

b. If your investment in 1905 has grown to $1 million, how much did you invest in 1905?

2. If the interest rate this year is 8.4% and the interest rate next year will be 10.4%, what is the future value of $1 after 2 years? What is the present value of a payment of $1 to be received in 2 years?

3. In mid-2010 a pound of apples cost $1.36, while oranges cost $1.20. Ten years earlier the price of apples was only $.97 a pound and that of oranges was $.75 a pound.

a. What was the annual compound rate of growth in the price of the two fruits?

b. If the same rates of growth persist in the future, what will be the price of apples in 2030?

c. What about the price of oranges?

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Solutions describe the steps to calculate present/future values and growth rates in the given cases.

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1. Investments in the stock market have increased at an average compound rate of about 5% since 1905. It is now 2012.

a. If you invested $1,000 in the stock market in 1905, how much would that investment be worth today?

Total number of periods=n=107 years
Average growth rate=r=5%
Amount invested in 1905=P=$1000
Amount accumulated in 2012=F=P*(1+r)^n=1000*(1+5%)^107=185,035.48

b. If your investment in 1905 has grown to $1 million, how much did ...

Solution provided by:
Lokesh Jain, MSc
Education
  • BEng (Hons) , Birla Institute of Technology and Science, India
  • MSc (Hons) , Birla Institute of Technology and Science, India
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