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Difficulty: EasyPercentages, Percent Change, and Interest

An investment fund had an initial value of $4000\$4{}000. During the first year, the value of the fund increased by 15%15\%. During the second year, the new value of the fund increased by 10%10\%. What was the total value of the fund at the end of the second year?

  1. $5060\$5{}060Answer
  2. B
    $5000\$5{}000
  3. C
    $4600\$4{}600
  4. D
    $4840\$4{}840
  5. E
    $5290\$5{}290

Answer

The total value of the fund at the end of the second year was $5060\$5{}060.
To find the final value after successive percent increases, compute the growth sequentially. After Year 1, the fund grows to $4000×1.15=$4600\$4{}000 \times 1.15 = \$4{}600. In Year 2, the 10%10\% increase applies to the new amount of $4600\$4{}600, resulting in $4600×1.10=$5060\$4{}600 \times 1.10 = \$5{}060. Thus, $5060\$5{}060 is the correct final value.

Step-by-Step Solution

1
Calculate the fund's value at the end of the first year.
$4000×(1+0.15)=$4000×1.15=$4600\$4{}000 \times (1 + 0.15) = \$4{}000 \times 1.15 = \$4{}600
A 15%15\% increase on the initial $4000\$4{}000 base increases the value to 115%115\% of its original amount.
2
Calculate the fund's value at the end of the second year using the updated base value.
$4600×(1+0.10)=$4600×1.10=$5060\$4{}600 \times (1 + 0.10) = \$4{}600 \times 1.10 = \$5{}060
The second year's 10%10\% increase applies to the new base value of $4600\$4{}600, not the initial $4000\$4{}000.

Key Concept

Successive Percent Changes and Base Shift
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Topics

Percentages, Percent Change, and Interest

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