3400 dollars is placed in an account with an annual interest rate of 7.5%. How much will be in the account after 17 years, to the nearest cent?

To solve this, we'll use the formula for compound interest, which is:

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

Where:
- $ A $ is the amount in the account after interest.
- $ P $ is the principal amount (initial investment) = $3400.
- $ r $ is the annual interest rate = 7.5% = 0.075.
- $ n $ is the number of times the interest is compounded per year (if not specified, we'll assume it's compounded annually, so $ n = 1 $).
- $ t $ is the number of years = 17.

Plugging in the values:

\[
A = 3400 \left(1 + \frac{0.075}{1}\right)^{1 \times 17}
\]

Now let me calculate this.After 17 years, the amount in the account will be approximately \$11,625.80.

Do you want any more details or have any questions?

Here are 5 related questions to explore:
1. What would the total amount be if the interest was compounded monthly instead of annually?
2. How much interest would be earned after 17 years?
3. How would the amount change if the interest rate was 6% instead of 7.5%?
4. What would the account balance be after 10 years instead of 17?
5. How much would you need to invest initially to reach \$20,000 after 17 years with the same interest rate?

**Tip:** Compounding more frequently (e.g., monthly) generally results in more interest earned than annual compounding.

Find out how to calculate compound interest on $3400 with an annual interest rate of 7.5% over 17 years. This problem involves applying the compound interest formula and understanding exponential growth. Suitable for students in Grades 9-12.

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