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Chapter 8: Problem 57

Suppose that you have \(\$ 10,000\) in a rather risky investment recommended by your financial advisor. During the first year, your investment decreases by \(30 \%\) of its original value. During the second year, your investment increases by \(40 \%\) of its first-year value. Your advisor tells you that there must have been a \(10 \%\) overall increase of your original \(\$ 10,000\) investment. Is your financial advisor using percentages properly? If not, what is your actual percent gain or loss of your original \(\$ 10,000\) investment?

Short Answer

Expert verified
NO, the financial advisor is not using the percentages properly. The actual percentage loss of the original investment is -2%.

Step by step solution

01

Calculate First Year Loss

The investment decreases by 30% in the first year. This can be calculated by finding 30% of $10,000, which is $3,000. So after the first year, the investment is worth $10,000 - $3,000 = $7,000.
02

Calculate Second Year Increase

The investment increases by 40% of the first-year value during the second year. 40% of $7,000 (the value after the first year) is $2,800. Therefore, at the end of the second year, the investment is worth $7,000 + $2,800 = $9,800.
03

Calculate Total Percentage Change

To determine the actual percentage gain or loss, find the difference between the final value ($9,800) and the initial value ($10,000), divide by the initial value, and multiply by 100%. This gives ((9,800-10,000)/10,000)*100% = -2%.
04

Comparison

This percentage should be compared with the 10% increase claimed by the financial advisor.

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Most popular questions from this chapter

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