Hannah puts $14,000 in a CD (Certificate of Deposit) for 5 years. She is paid a simple interest at an annual rate of 2.5%. (a) How much interest does she earn overall? (b) How much is the account worth at the end of the 5 years?

We are given the following information:
- Principal (initial deposit) $ P = 14,000 $ dollars
- Time $ t = 5 $ years
- Annual simple interest rate $ r = 2.5\% = 0.025 $

We will use the simple interest formula to solve the problem:

### Simple Interest Formula:
\[
I = P \times r \times t
\]
where:
- $ I $ is the interest earned,
- $ P $ is the principal,
- $ r $ is the annual interest rate (in decimal form),
- $ t $ is the time in years.

#### Part (a): How much interest does she earn overall?

Substitute the given values into the formula:

\[
I = 14,000 \times 0.025 \times 5 = 1,750
\]

So, Hannah earns **$1,750** in interest over 5 years.

#### Part (b): How much is the account worth at the end of the 5 years?

The total value of the account at the end of the period (the future value $ A $) is the sum of the principal and the interest:

\[
A = P + I = 14,000 + 1,750 = 15,750
\]

Thus, the account is worth **$15,750** at the end of 5 years.

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Would you like more details on these calculations or have any further questions?

Here are 5 related questions you might want to explore:
1. What is the difference between simple interest and compound interest?
2. How much interest would she earn if the interest rate were 3% instead of 2.5%?
3. How would the account balance change if Hannah invested for 10 years instead of 5?
4. What happens if the interest is compounded annually instead of simple interest?
5. How can Hannah calculate monthly interest payments instead of yearly?

**Tip**: Simple interest grows at a constant rate, while compound interest grows faster because interest is added to the principal periodically.

Learn how to calculate simple interest for an investment of $14,000 at a 2.5% annual rate over 5 years. This example demonstrates the use of the simple interest formula and provides a clear step-by-step solution, suitable for students in Grades 6-8.

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