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The formula given for the value of the investment after $ n $ years is:

\[
f(n) = 6000 \times (1.05)^n
\]

To find the value of the investment after 5 years, substitute $ n = 5 $ into the equation:

\[
f(5) = 6000 \times (1.05)^5
\]

Now calculate:

\[
f(5) = 6000 \times (1.2762815625) \approx 7657.69
\]

So, the value of the investment after 5 years is approximately **$7,657.69**.

Would you like more details or have any other questions?

Here are 5 related questions you can explore:
1. What would the investment value be after 10 years?
2. How would the formula change if the annual growth rate was 6% instead of 5%?
3. What would be the value if the initial investment was $10,000 instead of $6,000?
4. How many years would it take for the investment to double in value?
5. What is the continuous compound interest formula for a similar scenario?

**Tip:** To double-check your calculations, always round the result to the nearest cent for accuracy in financial contexts!

The value in dollars of a $6,000 investment after n years is given by f(n) = 6000(1.05)^n. Find the value of the investment (in dollars) after 5 years.

Calculate the future value of a $6,000 investment after 5 years using the formula f(n) = 6000(1.05)^n. Learn how exponential growth impacts investments and how to round to the nearest cent for financial accuracy.

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