Question

Suppose $4000 is invested at 6% interest compounded annually. Our formula is f(x) = 4000(1.06)^x is the number of years since the investment. How much money will there be in the bank at the end of 5 years Find f(5)

Answer 1

To find the amount of money in the bank at the end of 5 years using the given function \( f(x) = 4000(1.06)^x \), where \( x \) represents the number of years since the investment, we need to evaluate \( f(5) \).

Let's calculate \( f(5) \):

\[
f(5) = 4000(1.06)^5
\]

First, we need to calculate \( (1.06)^5 \):

\[
(1.06)^5 \approx 1.338225
\]

Now, substituting this back into the function:

\[
f(5) = 4000 \times 1.338225
\]

Calculating this gives:

\[
f(5) \approx 5352.90
\]

Thus, at the end of 5 years, there will be approximately \( \boxed{5352.90} \) dollars in the bank.