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 + )^ future amount = i(1 + r)^t

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 + )^ future amount = i(1 + r)^t

Answer

Explanation:

Step1: Identify the initial investment

The initial investment $I = 500$.

Step2: Determine the growth rate per 2 - year period

The growth rate $r=0.15$.

Step3: Calculate the number of 2 - year periods

The number of 2 - year periods in 40 years, $t=\frac{40}{2}=20$.

Step4: Use the compound - growth formula

The formula for future amount is $A = I(1 + r)^t$. Substitute $I = 500$, $r = 0.15$, and $t = 20$ into the formula: $A=500\times(1 + 0.15)^{20}$.

Step5: Calculate the result

$(1 + 0.15)^{20}\approx16.366537$. Then $A = 500\times16.366537=8183.2685\approx8183.27$.

Answer:

$8183.27$