Answer: $151377.5 should be invested.
Explanation:
The formula for continuously compounded interest is
A = P x e (r x t)
Where
A represents the future value of the investment after t years.
P represents the present value or initial amount invested
r represents the interest rate
t represents the time in years for which the investment was made.
e is the mathematical constant approximated as 2.7183.
From the information given,
A = $300000
r = 3.8% = 3.8/100 = 0.038
t = 18 years
Therefore,
300000 = P x 2.7183^(0.038 x 18)
300000 = P x 2.7183^(0.684)
300000 = 1.9818P
P = 300000/1.9818
P = $151377.5