Carlos invests $33,180 at 6% simple interest for 34 years. How much is in the account at the end of the 34-year period?  Round to the cent


To calculate the amount in Carlos' account at the end of the 34-year period, we use the formula for simple interest:

\[
A = P(1 + rt)
\]

Where:
- $ A $ is the total amount in the account after interest.
- $ P $ is the principal amount (initial investment).
- $ r $ is the annual interest rate (as a decimal).
- $ t $ is the time in years.

Given:
- $ P = 33,180 $
- $ r = 6\% = 0.06 $
- $ t = 34 $ years

Let's plug these values into the formula:

\[
A = 33,180(1 + 0.06 \times 34)
\]

Now, calculate $ A $.

\[
A = 33,180(1 + 2.04) = 33,180(3.04)
\]

\[
A = 100,867.20
\]

So, the total amount in the account after 34 years is **$100,867.20**.

Would you like any further details or clarifications?

Here are five related questions to consider:
1. How would the amount change if the interest rate were 5% instead of 6%?
2. What if Carlos had invested for only 20 years instead of 34?
3. How does simple interest differ from compound interest?
4. What happens to the total if the initial investment is increased by 10%?
5. How can you calculate the interest earned without calculating the total amount?

**Tip:** Simple interest grows linearly over time, unlike compound interest which grows exponentially.

Carlos invests $33,180 at 6% simple interest for 34 years. How much is in the account at the end of the 34-year period? Round to the cent.

Learn how to calculate simple interest using the formula A = P(1 + rt) with an example where Carlos invests $33,180 at 6% for 34 years. The total amount after 34 years is $100,867.20. Suitable for Grades 9-12, this problem covers key algebraic concepts.

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