Question

Following the birth of a child, a parent wants to make an initial investment Po that will grow to $50,000 for the child's

education at age 17. Interest is compounded continuously at 7%.
What should the initial investment be? Such an amount is called the present value of $50,000 due 17 years from now.
The present value is about $
(Do not round until the final answer. Then round to two decimal places as needed.)

Answer 1

The initial investment needed to grow to $50,000 in 17 years at a 7% annual interest rate compounded continuously is approximately $15,205.73.

Step-by-step explanation:

To find the present value of an investment that will grow to $50,000 at a 7% annual interest rate compounded continuously for 17 years, we use the formula for continuous compounding: PV = Pert where PV is the present value, P is the future value, r is the yearly interest rate, and t is the time in years. By rearranging the formula to solve for Po, we get:

Po = PV / ert

Plugging in the values:

Po = $50,000 / e0.07*17 = $50,000 / e1.19

Po is therefore approximately:

Po = $50,000 / e1.19 ≈ $50,000 / 3.28717 ≈ $15,205.73

The initial investment should be roughly $15,205.73.