17. How much money would you need to 
deposit today at 8% annual interest 
compounded monthly to have 
$10,000 in the account after 5 years? 
A. $6,500.5 
B. $6,680.13 
C. $6,712.10 
D. $5,989.3

This problem involves calculating the present value using the formula for compound interest:

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

Where:
- $ P $ is the present value (the amount to be deposited today),
- $ A $ is the future value ($10,000),
- $ r $ is the annual interest rate (8% or 0.08),
- $ n $ is the number of times interest is compounded per year (monthly, so $ n = 12 $),
- $ t $ is the number of years (5 years).

Now, let's substitute the given values into the formula:

\[
P = \frac{10000}{(1 + \frac{0.08}{12})^{12 \times 5}}
\]

I'll calculate that.The amount you would need to deposit today is approximately **$6,712.10**. So, the correct answer is **C. $6,712.10**.

Would you like further clarification or details on the calculation?

Here are some related questions to deepen your understanding:
1. How does the interest rate affect the amount needed to deposit?
2. What if the interest was compounded annually instead of monthly?
3. How would the required deposit change for a different time period, say 3 years?
4. What if the goal was $15,000 in 5 years at the same interest rate?
5. How do you calculate the interest earned over the 5 years?

**Tip:** Always check if the interest is compounded monthly, quarterly, or annually, as it affects the final calculation.

How much money would you need to deposit today at 8% annual interest compounded monthly to have $10,000 in the account after 5 years? A. $6,500.5 B. $6,680.13 C. $6,712.10 D. $5,989.3

Learn how to calculate the initial deposit required to reach $10,000 in 5 years with 8% annual interest compounded monthly. This compound interest problem is essential for understanding key financial mathematics concepts. Ideal for high school students studying algebra and exponential growth.

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