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Question

Difficulty: EasyRatios, Rates, and Percentages

An investment firm allocates a total of $60,000\$60,000 between two funds, Fund X and Fund Y, in the ratio of 3:23:2, respectively. Fund X yields an annual return of 10%10\%, while Fund Y yields an annual return of 15%15\%.

Which of the following correctly pairs the amount invested in Fund X with the total dollar return generated from both funds combined after one year?

  1.  halt$36,000\ halt{\$36,000} invested in Fund X, and $7,200\$7,200 total returnAnswer
  2. B
    $24,000\$24,000 invested in Fund X, and $7,200\$7,200 total return
  3. C
    $36,000\$36,000 invested in Fund X, and $6,000\$6,000 total return
  4. D
    $40,000\$40,000 invested in Fund X, and $8,000\$8,000 total return
  5. E
    $36,000\$36,000 invested in Fund X, and $9,000\$9,000 total return

Answer

The investment in Fund X is $36,000\$36,000, and the total dollar return from both funds combined is $7,200\$7,200.
The option stating '$36,000\$36,000 invested in Fund X, and $7,200\$7,200 total return' is correct because Fund X receives 3/53/5 of the $60,000\$60,000 total ($36,000\$36,000), generating $3,600\$3,600 at 10%10\%. Fund Y receives 2/52/5 of the total ($24,000\$24,000), generating $3,600\$3,600 at 15%15\%. The combined return is $3,600+$3,600=$7,200\$3,600 + \$3,600 = \$7,200.

Step-by-Step Solution

1
Determine the dollar amount allocated to each fund using the given ratio.
Fund X allocation: 33+2×$60,000=35×$60,000=$36,000\frac{3}{3+2} \times \$60,000 = \frac{3}{5} \times \$60,000 = \$36,000. Fund Y allocation: 25×$60,000=$24,000\frac{2}{5} \times \$60,000 = \$24,000.
The total ratio parts equal 3+2=53 + 2 = 5 parts.
2
Calculate the annual return for Fund X.
Fund X return: 10% of $36,000=0.10×$36,000=$3,60010\% \text{ of } \$36,000 = 0.10 \times \$36,000 = \$3,600.
Fund X yields a 10%10\% return on its invested capital.
3
Calculate the annual return for Fund Y.
Fund Y return: 15% of $24,000=0.15×$24,000=$3,60015\% \text{ of } \$24,000 = 0.15 \times \$24,000 = \$3,600.
Fund Y yields a 15%15\% return on its invested capital.
4
Sum the returns from both funds to find the total return.
Total combined return: \$3,600 + \$3,600 = \$7,200.
The total return is the sum of returns from Fund X and Fund Y.

Key Concept

Ratio Allocation and Weighted Percentage Rates
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Topics

Ratios, Rates, and Percentages

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