How much money will there be in an account at the end of 7 years if $\$ 17000$ is deposited at $5 \%$ interest compounded semi-annually? (Assume no withdrawals are made.) Use the formula $A=P\left(1+\frac{r}{n}\right)^{\text {tn }}$ for compound interest.
The amount after 7 years will be $\$$ (Round to the nearest cent as needed.)

Step 1 ：We are given an initial deposit of $17000, an interest rate of 5%, and semi-annual compounding. We are asked to find the amount of money in the account after 7 years. We can use the formula for compound interest, which is \(A=P\left(1+\frac{r}{n}\right)^{tn}\), 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 form).

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 ：Substituting the given values into the formula, we get:

Step 8 ：\(P = 17000\)

Step 9 ：\(r = 0.05\)

Step 10 ：\(n = 2\)

Step 11 ：\(t = 7\)

Step 12 ：Calculating the final amount, we get \(A = 24020.554956554017\)

Step 13 ：Rounding to the nearest cent, the final amount after 7 years will be \(\boxed{\$24020.55}\)