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 \(\boxed{\$24020.55}\)