A commercial property was purchased at an initial value of V dollars. In its first year, t… — GRE General Test

A commercial property was purchased at an initial value of $V$ dollars. In its first year, the value of the property increased by $25\%$ . In its second year, the property's value decreased by $20\%$ relative to its value at the end of the first year. In its third year, the value of the property increased by $15\%$ relative to its value at the end of the second year. If the value of the property at the end of the third year was $\$276,000$ , what was the initial purchase value $V$ , in dollars, of the property?

Answer: 240000 dollars

Answer

240000

Each percent change applies to the value at the end of the previous period. A

25\%

increase scales the value by

1.25

, a

20\%

decrease scales it by

0.80

, and a

15\%

increase scales it by

1.15

. The net multiplier is

1.25 \times 0.80 \times 1.15 = 1.15

. Solving

1.15V = 276,000

gives

V = 240,000

Step-by-Step Solution

Convert percent changes to growth and decay multiplier factors

Year 1 factor = 1.25, Year 2 factor = 0.80, Year 3 factor = 1.15

Percent changes are compounded by multiplying successive growth/decay factors.

Multiply the factors sequentially to express the final value in terms of initial value V

Final Value = V × 1.25 × 0.80 × 1.15 = 1.15V

Combining successive multipliers simplifies the relationship between original and final amounts.

Set the algebraic expression equal to $276,000 and solve for V

V = 276,000 / 1.15 = 240,000

Dividing the final value by the overall multiplier determines the original base value.

Key Concept

Successive Percent Changes and Base Shift

Estimated Time:1m 30s

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