Question

In the year 1985, a house was valued at $100,000. By the year 2005, the value had appreciated to $160,000. What was the annual growth rate between 1985 and 2005?

Options:
a) 5%
b) 6%
c) 7%
d) 8%

Answer 1

The precise annual growth rate of the house's value from 1985 to 2005 is approximately 2.329%, which is not one of the provided options. The closest option to this calculated rate is 5%.

Step-by-step explanation:

To calculate the annual growth rate of the house value, we can use the formula for compound annual growth rate (CAGR), which is:

CAGR = (FV / PV)^(1/n) - 1

where FV is the future value of the investment, PV is the present value, and n is the number of years.

In this case, the future value (FV) is $160,000, the present value (PV) is $100,000, and the time period (n) is 20 years (from 1985 to 2005).

Let's plug in the values:

CAGR = ($160,000 / $100,000)^(1/20) - 1

CAGR = (1.6)^(1/20) - 1

CAGR = (1.02329) - 1

CAGR = 0.02329

The annual growth rate is therefore approximately 2.329%, which is not listed in the given options. To find the rate that matches the options provided, you would need to round the number since the exact value is not an option. Thus, none of the options a) 5%, b) 6%, c) 7%, or d) 8% are correct based on the precise calculation. However, the growth rate that is closest to our calculation is option a) 5%.