Answer:
The present value (P) of $60,000 due 18 years from now can be calculated using the formula for continuous compounding:
P = A / e^(rt)
Where:
P = present value (initial investment)
A = future amount ($60,000)
r = annual interest rate (7% or 0.07 as a decimal)
t = time in years (18 years)
e = Euler's number (approximately 2.71828)
Substituting the given values into the formula:
P = 60000 / e^(0.07*18)
Calculating the value:
P ≈ 60000 / e^(1.26)
P ≈ 60000 / 3.5395
P ≈ 16947.61
Therefore, the initial investment (present value) should be approximately $16,947.61 to grow to $60,000 for the child's education at age 18, with continuous compounding at 7%.
Step-by-step explanation:
