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?\nfuture amount = 500(1 + 0.15)^{20}\nfuture amount = $?

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?\nfuture amount = 500(1 + 0.15)^{20}\nfuture amount = $?

Answer

Explanation:

Step1: Identify the number of 2 - year periods

The time period is 40 years. Since the growth occurs every 2 years, the number of 2 - year periods $n=\frac{40}{2}=20$.

Step2: Use the compound - growth formula

The formula for compound growth is $A = P(1 + r)^n$, where $P$ is the principal amount, $r$ is the growth rate per period, and $n$ is the number of periods. Here, $P = 500$, $r=0.15$, and $n = 20$. We need to calculate $A=500\times(1 + 0.15)^{20}$. First, calculate $(1 + 0.15)^{20}$. $(1 + 0.15)^{20}=1.15^{20}\approx16.366537$. Then, multiply by the principal amount: $A = 500\times16.366537=8183.2685\approx8183.27$.

Answer:

$8183.27$