How much money will there be in an account at the end of 10 years if $\$ 18000$ 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.

Step 1 ：We are given an initial deposit of $18000, an interest rate of 5% compounded semi-annually, and we are asked to find the amount of money in the account after 10 years. The formula for compound interest is given as \(A=P\left(1+\frac{r}{n}\right)^{tn}\) 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, so 5% would be 0.05).

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 ：We can substitute the given values into the formula and calculate the final amount.

Step 8 ：Let's substitute the values into the formula: P = 18000, r = 0.05, n = 2, t = 10.

Step 9 ：After substituting the values into the formula, we get the final amount in the account after 10 years to be approximately $29495.10.

Step 10 ：Final Answer: The amount of money in the account at the end of 10 years will be approximately \$29495.10. So, the final answer is \(\boxed{29495.10}\).