The formula for continuous compounding is:
A = Pe^(rt)
where:
A = the amount of money after t years,
P = the principal amount (initial investment),
e = the mathematical constant e (approximately equal to 2.71828),
r = the interest rate (in decimal form),
t = the time (in years).
Plugging in the given values, we get:
300000 = Pe^(0.036*14)
To solve for P, we need to isolate it on one side of the equation. We can start by dividing both sides by e^(0.036*14):
300000 / e^(0.036*14) = P
Using a calculator, we get:
300000 / e^(0.504) ≈ 142270.36
Rounded to the nearest cent, the amount of money that needs to be invested at an interest rate of 3.6% per year compounded continuously to amount to $300,000 after 14 years is $142,270.36.