Question

Mr. and Mrs. Hall hope to send their daughter to college in thirteen years. How much money should they invest now at an interest rate of 9% per year, compounded continuously, in order to be able to contribute $9500 to her education?

Answer 1

Mr. and Mrs. Hall should invest approximately $3137.81 now at an interest rate of 9% per year, compounded continuously, in order to be able to contribute $9500 to their daughter's education in thirteen years.

Step-by-step explanation:

To determine how much money Mr. and Mrs. Hall should invest now to contribute $9500 to their daughter's education in thirteen years, we can use the formula for compound interest. The formula for continuous compounding is given by: A = P*e^(r*t), where A is the future value, P is the principal amount, r is the interest rate per year, and t is the time in years. In this case, we are given A = $9500, r = 9%, and t = 13 years. Plugging these values into the formula, we can solve for P:

$9500 = P*e^(0.09*13)

P = $9500 / e^(0.09*13)

P ≈ $3137.81

Therefore, Mr. and Mrs. Hall should invest approximately $3137.81 now at an interest rate of 9% per year, compounded continuously, in order to be able to contribute $9500 to their daughter's education in thirteen years.