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?


To calculate the total amount in Ms. Zumberge's account after 3 years with interest compounded annually, we use the compound interest formula:

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

Where:
- $A$ is the total amount in the account after interest.
- $P$ is the principal (initial investment), which is $3,000.
- $r$ is the annual interest rate, which is 4% (or 0.04 as a decimal).
- $n$ is the number of times the interest is compounded per year. Since the interest is compounded annually, $n = 1$.
- $t$ is the time the money is invested for, which is 3 years.

Plugging the values into the formula:

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

\[
A = 3000 \left( 1.04 \right)^3
\]

Now, calculate $1.04^3$:

\[
1.04^3 = 1.124864
\]

Thus,

\[
A = 3000 \times 1.124864 = 3374.59
\]

So, the total amount in Ms. Zumberge's account after 3 years is **$3,374.59**.

Would you like more details or have any questions?

Here are 5 related questions to think about:
1. What if the interest was compounded semi-annually instead of annually?
2. How much interest did Ms. Zumberge earn after 3 years?
3. What would the total amount be if the interest rate was 5% instead of 4%?
4. How would the result change if she invested for 5 years instead of 3 years?
5. What if Ms. Zumberge invested $5,000 instead of $3,000 at the same interest rate?

**Tip**: The more frequently interest is compounded, the more total interest will be earned over time.

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?

Find out how to calculate the total amount in Ms. Zumberge's account after investing $3,000 at 4% interest, compounded annually, for 3 years. Learn how to apply the compound interest formula and understand key concepts of exponential growth. Suitable for students in Grades 9-11.

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