You deposit money into an account that earns simple interest at an annual rate of 8%. After 5 years, the account earns $1200 in interest. How much money did you deposit into the account?

To find out how much money was deposited into the account, we can use the formula for simple interest:

\[
I = P \times r \times t
\]

Where:
- $ I $ is the interest earned,
- $ P $ is the principal (initial amount deposited),
- $ r $ is the annual interest rate (in decimal form),
- $ t $ is the time in years.

Given:
- The interest earned ($ I $) is $1200,
- The annual interest rate ($ r $) is 8% or 0.08,
- The time ($ t $) is 5 years.

We need to find the principal ($ P $). Plugging the known values into the formula:

\[
1200 = P \times 0.08 \times 5
\]

Simplify the equation:

\[
1200 = P \times 0.4
\]

Now, solve for $ P $:

\[
P = \frac{1200}{0.4} = 3000
\]

So, the amount of money deposited into the account was **$3000**.

Would you like a detailed explanation, or do you have any questions?

Here are some related questions to further explore this topic:

1. How would the initial deposit change if the interest rate was 10% instead of 8%?
2. What would be the total amount in the account after 5 years, including both principal and interest?
3. How much interest would the account earn in 10 years at the same rate?
4. If the interest was compounded annually instead of being simple interest, how would the final amount differ?
5. How does the time period affect the amount of interest earned in simple interest?

**Tip:** When dealing with simple interest, the total interest earned is directly proportional to the principal, rate, and time period.

Learn how to calculate the initial deposit for an account earning simple interest at an annual rate of 8%. In this example, after 5 years, the account earns $1200 in interest. Find the step-by-step solution using the simple interest formula. Suitable for students in Grades 6-8.

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