A financial analyst is evaluating the long-term performance of four mutual funds. The aver… — State PSC Exam

A financial analyst is evaluating the long-term performance of four mutual funds. The average annualized yield rates of the funds are given below. Arrange the funds in descending order based on their yield rates (from highest to lowest).

1Fund X: $8 \frac{1}{6}\%$
2Fund Y: $8.1\overline{5}\%$
3Fund W: $8.\overline{15}\%$
4Fund Z: $\frac{57}{7}\%$

Answer

The correct descending order is Fund X, Fund Y, Fund W, then Fund Z.

By converting all values to their extended decimal forms, we determine their precise magnitudes: Fund X is

8.166...\%

, Fund Y is

8.155...\%

, Fund W is

8.151...\%

, and Fund Z is

8.142...\%

. Ordering these from highest to lowest yields Fund X, Fund Y, Fund W, then Fund Z.

Step-by-Step Solution

Convert Fund W's yield to extended decimal form for precise comparison.

Fund W =

8.\overline{15}\% = 8.1515...\%

Expanding the recurring decimals reveals the sequence of digits beyond the hundredths place.

Convert Fund X's yield to decimal form.

Fund X =

8 \frac{1}{6}\% = 8 + 0.1666...\% = 8.1666...\%

Converting the mixed fraction standardizes the format to match the others.

Convert Fund Y's yield to extended decimal form.

Fund Y =

8.1\overline{5}\% = 8.1555...\%

Properly expanding the specific repeating digit distinguishes it from Fund W.

Convert Fund Z's yield to decimal form.

Fund Z =

\frac{57}{7}\% = 8 \frac{1}{7}\% \approx 8.1428...\%

Division provides the decimal equivalent needed for a direct comparison.

Compare the decimal values digit by digit from left to right.

Highest is

8.166...

(Fund X), then

8.155...

(Fund Y), then

8.151...

(Fund W), and lowest is

8.142...

(Fund Z).

Sorting by the tenths, hundredths, and thousandths digits establishes the definitive descending sequence.

Key Concept

Converting mixed fractions, improper fractions, and different notations of recurring decimals into standard decimal form for accurate comparison.

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