Question
Suppose $4000 is invested at 6% interest compounded annually. Our formula is 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)=
$
round to the nearest cent
, 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)=
$
round to the nearest cent
Answers
GPT-4o mini
To find the amount of money in the bank at the end of 5 years using the formula \( f(x) = 4000(1.06)^x \), we need to evaluate \( f(5) \).
Substituting \( x = 5 \) into the formula:
\[
f(5) = 4000(1.06)^5
\]
Now, let's calculate \( (1.06)^5 \).
\[
(1.06)^5 \approx 1.338225
\]
Now, multiply this by 4000:
\[
f(5) = 4000 \times 1.338225 \approx 5353.00
\]
Thus, rounding to the nearest cent, we find:
\[
f(5) \approx 5353.00
\]
Therefore, the amount of money in the bank at the end of 5 years is:
\[
\boxed{5353.00}
\]
Substituting \( x = 5 \) into the formula:
\[
f(5) = 4000(1.06)^5
\]
Now, let's calculate \( (1.06)^5 \).
\[
(1.06)^5 \approx 1.338225
\]
Now, multiply this by 4000:
\[
f(5) = 4000 \times 1.338225 \approx 5353.00
\]
Thus, rounding to the nearest cent, we find:
\[
f(5) \approx 5353.00
\]
Therefore, the amount of money in the bank at the end of 5 years is:
\[
\boxed{5353.00}
\]