Question

Suppose $4000 is invested at 6% interest compounded annually. Our formula is f(x)=4000(1.06)x
𝑓
(
𝑥
)
=
4000
(
1.06
)
𝑥
, where 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)

(1 point)
f(5)=
𝑓
(
5
)
=
$ round to the nearest cent

Answer 1

To calculate the amount of money in the bank at the end of 5 years using the formula \( f(x) = 4000(1.06)^x \), we will substitute \( x = 5 \) into the equation.

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

Now, we will calculate \( (1.06)^5 \):

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

Now we can continue with the calculation:

\[
f(5) = 4000 \times 1.338225 \approx 5352.90
\]

Thus, rounding to the nearest cent:

\[
f(5) \approx \text{\$5352.90}
\]

Therefore, the amount of money in the bank at the end of 5 years is:

\[
\boxed{5352.90}
\]