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 = ?(1 + )^

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 = ?(1 + )^

Answer

Explanation:

Step1: Determine the initial amount

The initial investment is $500, so the first value in the formula is 500.

Step2: Determine the growth rate

The growth rate is 15% or 0.15.

Step3: Determine the number of 2 - year periods

There are 40 years. Since the growth occurs every 2 years, the number of 2 - year periods $n=\frac{40}{2}=20$. The formula for future amount $A = P(1 + r)^n$, where $P$ is the principal amount, $r$ is the growth rate per period, and $n$ is the number of periods. So the future amount formula for this problem is $A = 500(1+ 0.15)^{20}$. Now calculate $(1 + 0.15)^{20}$: Let $x=(1 + 0.15)^{20}=1.15^{20}$. Using a calculator, $1.15^{20}\approx16.3665$. Then $A = 500\times16.3665 = 8183.25$.

Answer:

$8183.25$