Question

When your parents got married 38 years ago, they purchased a house for $31,900. They have taken good care of the house but have not invested any more money into it. Today, their house is valued at $149,900. What rate of return have your parents earned on their home?

Answer 1

The average annual rate of return on your parents' home over the 38 years they owned it is approximately 3.53%.

Step-by-step explanation:

To calculate the rate of return on your parents' home, we'll use the formula for the average annual growth rate (AAGR):

AAGR = ((Ending value / Beginning value) ^ (1 / Number of years)) - 1

Applying this formula to the given values:

Beginning value = $31,900

Ending value = $149,900

Number of years = 38

So, AAGR = (($149,900 / $31,900) ^ (1 / 38)) - 1

First, we calculate the ratio of the ending value to the beginning value:

Ratio = $149,900 / $31,900 ≈ 4.7003

Next, we calculate the 38th root of the ratio:

38th root = 4.7003 ^ (1 / 38) ≈ 1.0353

The AAGR is then found by subtracting 1 from this value:

AAGR ≈ 1.0353 - 1 = 0.0353 or 3.53%

Your parents earned an average annual rate of return of approximately 3.53% on their home over the 38 years they owned it.