The Mendes family bought a new house 10 years ago for $101,000. The house is now worth $160,000. Assuming a steady rate of growth, what was the yearly rate of appreciation ?
let the rate be r
101(1 + r)^10 = 160
(1+r)^10 = 160/101 = 1.58418...
take 10th root of both sides to get
1+r
subtract 1 from that, then change to a percent
To find the yearly rate of appreciation, we need to calculate the compound annual growth rate (CAGR) between the initial value and the final value.
The formula to calculate CAGR is:
CAGR = (Final Value / Initial Value)^(1 / Number of Years) - 1
In this case, the initial value (IV) is $101,000, and the final value (FV) is $160,000. The number of years (N) is 10.
Now let's plug in the values and calculate the CAGR:
CAGR = ($160,000 / $101,000)^(1 / 10) - 1
We can simplify this calculation step by step:
First, divide the final value by the initial value:
160,000 / 101,000 = 1.5842
Next, divide 1 by the number of years:
1 / 10 = 0.1
Then, raise the result from the previous step to the power of the fraction:
1.5842^(0.1) = 1.0617
Finally, subtract 1 from the result and multiply by 100 to get the percentage:
(1.0617 - 1) * 100 = 6.17%
Therefore, the yearly rate of appreciation for the Mendes family's house is approximately 6.17%.