QuestionSeptember 19, 2025

Ten years after purchasing 8,000 worth of shares in a mutual fund, you sell the shares for 6,850 (at a loss). Find the annual return (to the nearest hundredth of a percent) on your investment. -1.44% % -1.54% % -1.24% % -1.89% % None of the above.

Ten years after purchasing 8,000 worth of shares in a mutual fund, you sell the shares for 6,850 (at a loss). Find the annual return (to the nearest hundredth of a percent) on your investment. -1.44% % -1.54% % -1.24% % -1.89% % None of the above.
Ten years after purchasing 8,000 worth of shares in a mutual fund, you sell the shares for 6,850 (at a loss). Find the annual return (to the nearest hundredth of a percent) on your investment.
-1.44% % 
-1.54% % 
-1.24% % 
-1.89% % 
None of the above.

Solution
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Answer

-1.54\% Explanation 1. Use the Compound Annual Growth Rate (CAGR) Formula The CAGR formula is r = \left(\frac{A}{P}\right)^{1/n} - 1, where A = \6,850, P = \8,000, n = 10. 2. Substitute Values and Calculate r = \left(\frac{6850}{8000}\right)^{1/10} - 1 = (0.85625)^{0.1} - 1 3. Compute the Result (0.85625)^{0.1} \approx 0.98456, so r = 0.98456 - 1 = -0.01544 4. Convert to Percentage and Round -0.01544 \times 100 = -1.54\%

Explanation

1. Use the Compound Annual Growth Rate (CAGR) Formula<br /> The CAGR formula is $r = \left(\frac{A}{P}\right)^{1/n} - 1$, where $A = \$6,850$, $P = \$8,000$, $n = 10$.<br />2. Substitute Values and Calculate<br /> $r = \left(\frac{6850}{8000}\right)^{1/10} - 1 = (0.85625)^{0.1} - 1$<br />3. Compute the Result<br /> $(0.85625)^{0.1} \approx 0.98456$, so $r = 0.98456 - 1 = -0.01544$<br />4. Convert to Percentage and Round<br /> $-0.01544 \times 100 = -1.54\%$
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