18. A couple is opening a savings account for a newborn baby. They start with $\$ 3,450$ received in baby gifts. If no deposits or withdrawals are made, what is the balance of the account if it earns simple interest at $5 \%$ for 18 years?
Solution
Step 1 ：The problem is asking for the balance of a savings account after 18 years with a starting balance of $3450 and an annual interest rate of 5%. This is a simple interest problem, so we can use the formula for simple interest to solve it.
Step 2 ：The formula for simple interest is: \[A = P(1 + rt)\] where: \[A\] 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), and \[t\] is the time the money is invested for, in years.
Step 3 ：In this case, \[P = 3450\], \[r = 5\% = 0.05\], and \[t = 18\] years. We can substitute these values into the formula to find the final balance of the account.
Step 4 ：Substituting the values into the formula, we get: \[A = 3450(1 + 0.05 \times 18)\]
Step 5 ：Solving the equation, we find that \[A = 6555.0\]
Step 6 ：Final Answer: The balance of the account after 18 years will be \(\boxed{6555}\)
