A commercial real estate developer purchases a building. In the first year after purchase,… — GMAT

A commercial real estate developer purchases a building. In the first year after purchase, the value of the building increases by $40\%$ . In the second year, the value decreases by $25\%$ from its first-year value. In the third year, the value increases by $20\%$ from its second-year value. If the value of the building at the end of the third year is $\$630,000$ , what was the original purchase price of the building?

A
$\$375,000$
B
$\$378,000$
C
$\$450,000$
$\$500,000$ Answer
E
$\$525,000$

Answer

The original purchase price of the building was

\$500,000

To find the original price, express each sequential percent change as a multiplier applied to the preceding value. A

40\%

increase corresponds to a factor of

1.40

, a

25\%

decrease corresponds to a factor of

0.75

, and a

20\%

increase corresponds to a factor of

1.20

. Combining these gives a overall multiplier of

1.40 \times 0.75 \times 1.20 = 1.26

. Setting

1.26 \times P = \$630,000

yields

P = \$500,000

Step-by-Step Solution

Express each annual percentage change as a multiplier factor.

Year 1 increase of

40\% \rightarrow 1 + 0.40 = 1.40 = \frac{7}{5}

. Year 2 decrease of

25\% \rightarrow 1 - 0.25 = 0.75 = \frac{3}{4}

. Year 3 increase of

20\% \rightarrow 1 + 0.20 = 1.20 = \frac{6}{5}

Successive percentage changes compound sequentially on the updated intermediate values.

Calculate the cumulative multiplier over the three-year period.

\text{Overall Multiplier} = 1.40 \times 0.75 \times 1.20 = \frac{7}{5} \times \frac{3}{4} \times \frac{6}{5} = \frac{126}{100} = 1.26.

Multiplying individual year multipliers yields the net scale factor from the initial price to the final value.

Set up the linear equation for the initial price

P

and solve.

1.26 \times P = 630,000 \implies P = \frac{630,000}{1.26} = 500,000.

Dividing the final valuation by the overall multiplier determines the original purchase price.

Key Concept

Successive Percent Change

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

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