Ms. Zumberge invested $3,000 at an interest rate of 4%, compounded annually, for 3 years.

What is the total amount in Ms. Zumberge’s account after 3 years?   How much interest is earned?

To solve this, we'll use the **compound interest formula**:

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

Where:
- $A$ is the amount in the account after interest.
- $P$ is the principal (initial investment).
- $r$ is the annual interest rate (in decimal form).
- $n$ is the number of times the interest is compounded per year.
- $t$ is the time the money is invested for (in years).

Given:
- $P = 3000$
- $r = 4\% = 0.04$
- $n = 1$ (since it is compounded annually)
- $t = 3$ years

Now, let's calculate:

\[
A = 3000 \left(1 + \frac{0.04}{1}\right)^{1 \times 3}
\]
\[
A = 3000 \left(1.04\right)^3
\]

Next, I'll compute the result.The total amount in Ms. Zumberge’s account after 3 years is **$3,374.59**. The interest earned over this period is **$374.59**.

Would you like further details or have any questions?

Here are 5 related questions:
1. What would the total amount be if the interest rate were 5% instead of 4%?
2. How would the total amount change if the interest were compounded quarterly?
3. What is the difference in total interest earned if the investment period is extended to 5 years?
4. How much would be earned if $5,000 were invested at the same interest rate for 3 years?
5. What is the future value if the interest is compounded monthly instead of annually?

**Tip:** Compounding more frequently (e.g., monthly or quarterly) will result in a higher total amount than annual compounding at the same rate.

Ms. Zumberge invested $3,000 at an interest rate of 4%, compounded annually, for 3 years. What is the total amount in Ms. Zumberge’s account after 3 years? How much interest is earned?

Calculate the total amount and interest earned for an investment of $3,000 at 4% interest compounded annually over 3 years. Learn how to use the compound interest formula to find the final amount of $3,374.59 and the interest earned of $374.59. Suitable for Grades 9-12.

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