investments increase exponentially by about 15% every 2 years. if you start with a $500 investment, how much…

investments increase exponentially by about 15% every 2 years. if you start with a $500 investment, how much money would you have after 40 years? future amount = 500(1 + 0.15)^20 future amount = $? round your answer to the nearest whole

investments increase exponentially by about 15% every 2 years. if you start with a $500 investment, how much money would you have after 40 years? future amount = 500(1 + 0.15)^20 future amount = $? round your answer to the nearest whole

Answer

Explanation:

Step1: Identify the formula components

The formula for compound - growth is $A = P(1 + r)^n$, where $P = 500$ (initial investment), $r=0.15$ (growth rate per 2 - year period), and $n$ is the number of 2 - year periods.

Step2: Calculate the number of 2 - year periods

Since the time period is 40 years and the growth occurs every 2 years, $n=\frac{40}{2}=20$.

Step3: Calculate the future amount

$A = 500\times(1 + 0.15)^{20}$. First, calculate $(1 + 0.15)^{20}$. Using a calculator, $(1.15)^{20}\approx16.366537$. Then, $A = 500\times16.366537 = 8183.2685$.

Step4: Round the answer

Rounding $8183.2685$ to the nearest whole number gives $8183$.

Answer:

$8183$