$4000 are invested in a bank account at an interest rate of 5 percent per year.


The problem you have provided involves calculating the growth of an investment in a bank account at a 5% interest rate per year. To solve this, we need to clarify whether the interest is simple or compound.

### 1. Simple Interest
In simple interest, the interest is calculated only on the initial principal amount. The formula for simple interest is:

\[
A = P(1 + rt)
\]

where:
- $ A $ is the final amount after time $ t $,
- $ P $ is the principal (initial investment),
- $ r $ is the annual interest rate (in decimal form),
- $ t $ is the time in years.

If $ P = 4000 $, $ r = 0.05 $, and $ t = 1 $ (assuming 1 year), the final amount will be:

\[
A = 4000(1 + 0.05 \times 1) = 4000(1 + 0.05) = 4000 \times 1.05 = 4200
\]

### 2. Compound Interest
For compound interest, the interest is calculated on the accumulated amount (principal + interest). The formula is:

\[
A = P \left( 1 + \frac{r}{n} \right)^{nt}
\]

where:
- $ n $ is the number of times the interest is compounded per year,
- The other variables are the same as above.

If the interest is compounded annually, then $ n = 1 $, and for 1 year:

\[
A = 4000 \left( 1 + \frac{0.05}{1} \right)^{1 \times 1} = 4000 \times 1.05 = 4200
\]

If compounded quarterly ($ n = 4 $):

\[
A = 4000 \left( 1 + \frac{0.05}{4} \right)^{4 \times 1} = 4000 \times \left( 1.0125 \right)^4 \approx 4203.14
\]

Would you like to know more about a specific case (e.g., compound interest over multiple years or different compounding periods)?

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Here are some related questions:
1. What happens if the interest rate increases or decreases?
2. How do different compounding periods (monthly, quarterly, etc.) affect the final amount?
3. What is the effect of leaving the investment in the account for more than 1 year?
4. How does the formula for compound interest change if interest is compounded continuously?
5. How does inflation impact the real value of the investment?

**Tip:** When investing, always check how frequently the interest compounds—this can significantly affect the growth of your investment.

$4000 are invested in a bank account at an interest rate of 5 percent per year.

Explore how to calculate the future value of a $4000 investment with a 5% annual interest rate. Learn the difference between simple and compound interest, including how compounding frequency affects the final amount. This solution covers key financial math concepts, formulas, and provides examples for annual and quarterly compounding.

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