What will a 180 000$ house cost 4years from now if the price appreciation for homes over that period averages 3% compounded annually?
To find out the cost of the house 4 years from now, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the house
P = the initial price of the house ($180,000)
r = the annual interest rate (3%)
n = the number of times the interest is compounded per year (assuming it's compounded annually)
t = the number of years (4 years)
Plugging the values into the formula:
A = 180,000(1 + 0.03/1)^(1*4)
Simplifying the equation:
A = 180,000(1 + 0.03)^4
Calculating:
A ≈ 180,000(1.03)^4
A ≈ 180,000(1.125508)
A ≈ $202,991.59
Therefore, the cost of the house 4 years from now would be approximately $202,991.59.
To calculate the future value of a $180,000 house after 4 years with a 3% annual compound appreciation rate, we can use the formula for compound interest:
Future Value = Present Value * (1 + Interest Rate)^Number of Periods
In this case, the Present Value (P) is $180,000, the Interest Rate (r) is 3% (or 0.03), and the Number of Periods (n) is 4 years.
Future Value = $180,000 * (1 + 0.03)^4
Now, let's calculate the future value of the house step-by-step:
Step 1: Calculate the interest rate plus 1:
(1 + 0.03) = 1.03
Step 2: Raise that sum to the power of the number of periods:
1.03^4 = 1.1255
Step 3: Multiply the present value by the result:
$180,000 * 1.1255 = $202,590
Therefore, a $180,000 house will cost approximately $202,590 four years from now with a 3% annual compound appreciation rate.
To determine the cost of the $180,000 house 4 years from now with a 3% annual appreciation rate, you can calculate the future value of the house using compound interest.
The formula for compound interest is:
Future Value = Present Value * (1 + interest rate)^(number of periods)
In this case, the present value (P) is $180,000, the interest rate (r) is 3%, and the number of periods (n) is 4 years.
Plugging in the values, the formula becomes:
Future Value = $180,000 * (1 + 0.03)^4
Now let's calculate the future value:
Future Value = $180,000 * (1.03)^4
Future Value = $180,000 * 1.1255
Future Value ≈ $202,590.43
Therefore, the estimated cost of the $180,000 house 4 years from now, with a 3% annual appreciation rate, would be approximately $202,590.43.