Question

A house was valued at $100,000 in the year 1987. The value appreciated to $165,000 by the year 2002.

Answer 1

Answer:

  A) The annual multiplier was 1.0339; the annual increase was 0.0339 of the value.

  B) 3.39% per year

  C) $182,000

Step-by-step explanation:

A) Let's let t represent years since 1987. Then we can fill in the numbers and solve for r.

  165000 = 100000(1 +r)^15

  1.65^(1/15) = 1 +r . . . . . divide by 100,000; take the 15th root

  1.03394855265 -1 = r ≈ 0.0339

The value was multiplied by about 1.0339 each year.

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B) The value increased by about 3.39% per year.

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C) S = $100,000(1.03394855265)^18 ≈ $182,000