Sue deposited $10,250 in a 20-year CD at Centre County Bank.  If the interest rate is 4.25% compounded annually, how much total interest will she earn?


We can solve this problem using the **compound interest formula**:

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

Where:
- $A$ is the final amount after interest,
- $P$ is the principal (initial deposit),
- $r$ is the annual interest rate (as a decimal),
- $n$ is the number of times interest is compounded per year,
- $t$ is the number of years.

### Given:
- $P = 10,250$,
- $r = 4.25\% = 0.0425$,
- $n = 1$ (since it's compounded annually),
- $t = 20$ years.

#### Step 1: Calculate the final amount, $A$:

\[
A = 10,250 \left(1 + \frac{0.0425}{1}\right)^{1 \times 20}
\]
\[
A = 10,250 \left(1 + 0.0425\right)^{20}
\]
\[
A = 10,250 \times (1.0425)^{20}
\]

Now let's compute $A$.The final amount $A$ after 20 years is approximately $23,563.79.

#### Step 2: Calculate the total interest earned:
\[
\text{Total Interest} = A - P
\]
\[
\text{Total Interest} = 23,563.79 - 10,250 = 13,313.79
\]

Sue will earn a total interest of approximately **$13,313.79**.

Would you like any further details or clarifications?

Here are 5 related questions:
1. What if the interest were compounded quarterly instead of annually?
2. How does the compound interest formula differ from simple interest?
3. What would the total interest be if the rate were 5% instead?
4. How much more interest would Sue earn if she invested for 25 years?
5. How does the frequency of compounding affect the interest earned?

**Tip**: Increasing the frequency of compounding (e.g., quarterly vs annually) increases the total interest earned over the same period.

Sue deposited $10,250 in a 20-year CD at Centre County Bank. If the interest rate is 4.25% compounded annually, how much total interest will she earn?

Calculate the total interest earned on a $10,250 investment over 20 years at an interest rate of 4.25% compounded annually. This problem uses the compound interest formula and covers essential concepts like exponential growth. Suitable for Grades 9-12 students.

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