Question Show Examples 3400 dollars is placed in an account with an annual interest rate of $8.25 \%$. How much will be in the account after 25 years, to the nearest cent? Answer Attempt 2 out of 2 Submit Answer

Step 1 ：This is a compound interest problem. The formula for compound interest is \(A = P(1 + r/n)^{nt}\), where:

Step 2 ：\(A\) is the amount of money accumulated after n years, including interest.

Step 3 ：\(P\) is the principal amount (the initial amount of money).

Step 4 ：\(r\) is the annual interest rate (in decimal).

Step 5 ：\(n\) is the number of times that interest is compounded per year.

Step 6 ：\(t\) is the time the money is invested for in years.

Step 7 ：In this case, \(P = 3400\), \(r = 8.25/100 = 0.0825\) (converted from percentage to decimal), \(n = 1\) (since it's annual interest), and \(t = 25\).

Step 8 ：Substitute the values into the formula: \(A = 3400(1 + 0.0825/1)^{(1*25)}\)

Step 9 ：Solving the equation gives \(A = 24670.42\)

Step 10 ：Final Answer: The amount in the account after 25 years, to the nearest cent, will be \(\boxed{24670.42}\).