Step 1 :Given values are: final amount \(A = \$7500\), annual interest rate \(r = 9.5\% = 0.095\) in decimal, and time \(t = 14\) years.
Step 2 :We need to find the initial amount \(P\) that should be invested now.
Step 3 :We use the formula for continuous compounding, which is \(A = Pe^{rt}\).
Step 4 :Rearranging the formula to solve for \(P\), we get \(P = \frac{A}{e^{rt}}\).
Step 5 :Substituting the given values into the formula, we get \(P = \frac{7500}{e^{0.095 \times 14}}\).
Step 6 :Calculating the above expression, we get \(P \approx \$1983.58\).
Step 7 :\(\boxed{\text{Final Answer: The initial amount that Mr. and Mrs. Phillips should invest now is approximately \$1983.58.}}\)