tim purchased a piece of land for $21,225. his realtor estimates that this piece of land will increase in…

tim purchased a piece of land for $21,225. his realtor estimates that this piece of land will increase in value by approximately 3.5% per year. what is the best estimate of the value of this piece of land 5 years after tim purchased it? $17,762 $25,209 $95,174 $24,356

tim purchased a piece of land for $21,225. his realtor estimates that this piece of land will increase in value by approximately 3.5% per year. what is the best estimate of the value of this piece of land 5 years after tim purchased it? $17,762 $25,209 $95,174 $24,356

Answer

Explanation:

Step1: 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 annual growth rate as a decimal, and $t$ is the number of years.

Step2: Convert the percentage to a decimal

The growth rate $r=3.5% = 0.035$, $P = 21225$, and $t = 5$.

Step3: Substitute the values into the formula

$A=21225\times(1 + 0.035)^5=21225\times(1.035)^5$.

Step4: Calculate $(1.035)^5$

$(1.035)^5=1.035\times1.035\times1.035\times1.035\times1.035\approx1.187686$.

Step5: Calculate the final value of $A$

$A = 21225\times1.187686\approx25209$.

Answer:

$25,209$