Question

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

Use the compound interest form S=P(1+r)^t to answer the following questions.
A) What was the annual growth rate between 1987 and 2002? (Round to 4 decimal places.)
B) What is the correct answer to part A written in percentage form?
C) Assume that the house value continues to grow by the same percentage. What will the value equal in the year 2005? (Round to the nearest thousand dollars.)
Please help ASAP I need an answer by today!!! :(

Answer 1

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

B) 3.39% per year

C) $182,000

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