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 problem, we will use the formula for compound interest, which is A = P(1 + r/n)^(nt).

Here's what each symbol stands for:

• 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 (in decimal form, so 7.5% becomes 0.075).
• n is the number of times that interest is compounded per year.
• t is the time the money is invested for in years.

In this case, the problem doesn't specify how often the interest is compounded. If it's not stated, it's usually assumed to be compounded once a year. So n would be 1.

Now we can plug the numbers into the formula:

A = 3400(1 + 0.075/1)^(1*17)

This simplifies to:

A = 3400(1 + 0.075)^17

Now, calculate the value inside the parentheses:

1 + 0.075 = 1.075

So the equation now is:

A = 3400 * (1.075)^17

Now, calculate the exponent:

(1.075)^17 ≈ 3.379

So the equation now is:

A = 3400 * 3.379

Finally, multiply the principal amount by the calculated value:

A = 11488.6

So, after 17 years, there will be approximately $11488.60 in the account, to the nearest cent.