The formula for continuous compounding is A = Pe^(rt), where A is the amount of money at the end of the investment period, P is the principal amount invested, e is the mathematical constant approximately equal to 2.71828, r is the annual interest rate, and t is the time in years.
In this case, we know that the Davises want to contribute $9500 to their son's education in 12 years, the annual interest rate is 9.5%, and the interest is compounded continuously. We can use this information to solve for the principal amount they should invest now.
A = Pe^(rt)
9500 = P*e^(0.095*12)
9500 = P*e^1.14
P = 9500/e^1.14
P = 9500/3.125
P = $3040.00 (rounded to the nearest cent)
Therefore, the Davises should invest $3040.00 now at an interest rate of 9.5% per year, compounded continuously, in order to be able to contribute $9500 to their son's education in 12 years.