To find the amount of money you must invest now at 4.8% interest compounded continuously to have $10,000 at the end of 5 years, we use the formula for continuously compounded interest:
A = P * e^(rt)
Where:
A = Future value (amount you want to have at the end of 5 years) = $10,000
P = Present value (amount you need to invest now)
e = Euler's number (approximately 2.71828)
r = Annual interest rate = 4.8% = 0.048 (in decimal form)
t = Time in years = 5 years
Substitute the given values into the formula:
$10,000 = P * e^(0.048*5)
$10,000 = P * e^(0.24)
Divide both sides by e^0.24:
P = $10,000 / e^0.24
P ≈ $10,000 / 1.271056
P ≈ $7,866.66
You must invest approximately $7,866.66 now at 4.8% interest compounded continuously to have $10,000 at the end of 5 years.
