you have inherited land that was purchased for $30,000 in 1960. the value of the land increased by…

you have inherited land that was purchased for $30,000 in 1960. the value of the land increased by approximately 5% per year. what is the approximate value of the land in the year 2010? write and solve the equation 30,000 (1 - 5)^50 --- $242,484.38 30,000 (1 + 5)^50 --- $344,021.99 30,000 (1 -.05)^50 --- $2,308.35 30,000 (1 +.05)^50 --- $344,021.99

you have inherited land that was purchased for $30,000 in 1960. the value of the land increased by approximately 5% per year. what is the approximate value of the land in the year 2010? write and solve the equation 30,000 (1 - 5)^50 --- $242,484.38 30,000 (1 + 5)^50 --- $344,021.99 30,000 (1 -.05)^50 --- $2,308.35 30,000 (1 +.05)^50 --- $344,021.99

Answer

Answer:

$30000(1 + 0.05)^{50}\approx$344,021.99$

Explanation:

Step1: Determine the time - period

The time from 1960 to 2010 is $2010 - 1960=50$ years.

Step2: Identify the compound - growth formula

The formula for compound growth is $A = P(1 + r)^t$, where $P$ is the initial amount, $r$ is the rate of growth as a decimal, and $t$ is the number of time - periods. Here, $P = 30000$, $r=0.05$ (since 5% = 0.05), and $t = 50$.

Step3: Calculate the final value

Substitute the values into the formula: $A=30000(1 + 0.05)^{50}$. Using a calculator, $(1 + 0.05)^{50}\approx11.467397$, and $30000\times11.467397\approx344021.99$.