Question

In: Statistics and Probability

Your boss tells you that his investment lost 20% during the first quarter (from Jan 1st-...

Your boss tells you that his investment lost 20% during the first quarter (from Jan 1st- March 31st), another 20% during the second quarter (from Apr 1st-June 30th) and then another 20% during the third quarter (from July 1st - Sept 30th). He then states "IO can't believe my investments lost 60% from Jan 1st- Sept 30th. What is wrong with this statement? What percent did he really lose?

Solutions

Expert Solution

Let X be the investment made by the boss at the beginning of the quarter.

The investment lost 20% during the first quarter. The amount lost is

0.20*X

The value of the investment at the end the first quarter would be

The value of the investment at the beginning of the second quarter is

Value(Q1) =0.80X

This lost 20% during the second quarter. The value of the investment at the end of the second quarter is

The value of the investment at the beginning of the third quarter is

This lost 20% during the third quarter. The value of the investment at the end of the third quarter is

The boss started with an investment of X at the beginning of  quarter 1 and ended up with 0.512X at the end of quarter 3.

The percentage of amount he lost is

ans: He really lost 48.8% of the investment and not 60% as he claimed.

The reason is the he lost 20% of the initial investment only in quarter 1, but in quarter 2 and quarter 3, he lost 20% of the value of the investment at the beginning of each quarter, which are of lesser value than the first quarter.

orchestra answered 2 years ago
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