Investing $10,000 in a savings account at 5% annual interest compounded semiannually will result in approximately how much money after 10 years?

Use the formula: A=P(1+r/m)^(mt)

$16,386.16

$16,288.95

$15,000.00

$13,448.89

We can solve this using the compound interest formula:

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

Where:
- $ P $ is the initial principal (amount of money invested) = $10,000
- $ r $ is the annual interest rate = 5% = 0.05
- $ m $ is the number of times the interest is compounded per year = 2 (since it is compounded semiannually)
- $ t $ is the time in years = 10 years

Now, plugging in the values:

\[
A = 10000 \left(1 + \frac{0.05}{2}\right)^{2 \times 10}
\]
\[
A = 10000 \left(1 + 0.025\right)^{20}
\]
\[
A = 10000 \left(1.025\right)^{20}
\]

Let's calculate $ A $.The amount after 10 years is approximately **$16,386.16**.

So, the correct answer is **$16,386.16**.

Would you like more details or have any questions?

Here are 5 related questions you might find interesting:
1. How does changing the compounding frequency affect the final amount?
2. What would happen if the interest rate were 6% instead of 5%?
3. How much more would the amount be if compounded quarterly instead of semiannually?
4. What would be the result after 15 years with the same conditions?
5. How much interest is earned after 10 years with this setup?

**Tip:** The more frequently interest is compounded, the higher the total amount grows.

Investing $10,000 in a savings account at 5% annual interest compounded semiannually will result in approximately how much money after 10 years?

Discover how to calculate compound interest on $10,000 invested at 5% annual interest compounded semiannually. Using the formula A = P(1 + r/m)^(mt), the final amount after 10 years is approximately $16,386.16. This detailed breakdown is suitable for students in Grades 10-12.

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