Trinh invested $3400 at 9%/a compounded annually. How much will she have in the investment account at the end of 6 years?
Question 1 options:

a)

$5702.14

b)

$1836.00

c)

$2302.14

d)

$5236.00

To determine how much Trinh will have in her investment account at the end of 6 years with an initial investment of $3400 at an annual interest rate of 9% compounded annually, we use the compound interest formula:

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

Where:
- $ A $ is the amount of money accumulated after n years, including interest.
- $ P $ is the principal amount (the initial amount of money).
- $ r $ is the annual interest rate (decimal).
- $ n $ is the number of times that interest is compounded per year.
- $ t $ is the time the money is invested for in years.

Given:
- $ P = 3400 $
- $ r = 9\% = 0.09 $
- $ n = 1 $ (since interest is compounded annually)
- $ t = 6 $

Plugging these values into the formula:

\[ A = 3400 \left(1 + \frac{0.09}{1}\right)^{1 \times 6} \]
\[ A = 3400 \left(1 + 0.09\right)^6 \]
\[ A = 3400 \left(1.09\right)^6 \]

Now we calculate $ 1.09^6 $:

\[ 1.09^6 \approx 1.6771 \]

So,

\[ A = 3400 \times 1.6771 \]
\[ A \approx 5702.14 \]

Thus, Trinh will have approximately $5702.14 in her investment account at the end of 6 years.

The correct answer is:

a) $5702.14

Would you like more details or have any questions?

Here are 5 more questions you can ask:

1. How do you calculate compound interest for different compounding periods?
2. What is the formula for continuous compound interest?
3. How does compound interest differ from simple interest?
4. Can you explain the Rule of 72 in finance?
5. What happens to the final amount if the interest rate changes during the investment period?

**Tip:** Always double-check the compounding frequency in compound interest problems, as it significantly affects the final amount.

Learn how to calculate compound interest for an initial investment of $3400 at an annual interest rate of 9% compounded annually over 6 years. Follow a step-by-step solution using the compound interest formula. Suitable for high school students and learners.

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