A house was valued at $125,000 in the year 1987. The value appreciated to $175,000 by the year 2002.
A) What was the annual growth rate between 1987 and 2002?
r= (round the growth rate to 4 decimal places)
B) What is the correct answer to part A written in percentage form?
r=
C) Assume that the house value continues to grow by the same percentage. What will the value equal in the year 2005?
value=$ (round to the nearest thousand dollars)
hi what grade is this
im gussing 10th oor 11th idk
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College
15 years, so
125000 * (1+r)^15 = 175000
r = 0.0227 = 2.27%
175K * 1.0227^3 = 187190
To find the annual growth rate between 1987 and 2002, we need to calculate the average annual growth rate.
A) To calculate the annual growth rate, we use the formula:
Annual growth rate (r) = (Ending value / Starting value)^(1 / Number of years) - 1
In this case, the starting value is $125,000 in 1987, and the ending value is $175,000 in 2002. The number of years is 2002 - 1987 = 15 years.
Plugging in the values:
r = ($175,000 / $125,000)^(1 / 15) - 1
Calculating this expression, we get:
r ≈ 0.0322 (rounded to 4 decimal places)
So, the annual growth rate between 1987 and 2002 is approximately 0.0322.
B) To convert the annual growth rate into percentage form, we multiply it by 100:
r_percentage = r * 100
Plugging in the value of r:
r_percentage ≈ 0.0322 * 100
Calculating this expression, we get:
r_percentage ≈ 3.22%
So, the correct answer in percentage form for part A is approximately 3.22%.
C) To find the value in the year 2005, we need to calculate the value after three years of growth from 2002.
Since the house value continues to grow by the same percentage, we can use the formula:
Future value = Present value * (1 + r)^(Number of years)
In this case, the present value is $175,000, the annual growth rate (r) is approximately 0.0322, and the number of years is 2005 - 2002 = 3 years.
Plugging in the values:
Future value = $175,000 * (1 + 0.0322)^3
Calculating this expression, we get:
Future value ≈ $192,625
So, the value of the house in the year 2005 would be approximately $192,625 (rounded to the nearest thousand dollars).