Question

If $5,000,000 is invested at 4% interest compound continuously how much will the investment be worth in 30 years

Answer 1

The formula for continuously compounding is  $A(t)=Pe^{rt}$, where P is the initial investment amount, e is Euler's number, r is the interest rate in decimal form, and t is the time in years.  For us that looks like this:  $A(t)=5,000,000e^{(.04)(30)}$.  Simplifying a bit gives us  $A(t)=5,000,000e^{1.2}$.  There is a button on your calculator to find the value of e^1.2.  Hit 2nd then ln and you'll see "e^  " on your display.  Enter 1.2 and hit "enter" to get that e^1.2 is equal to 3.320116923.  Now multiply that by your P value of 5 million to get A(t) = $16,600,584.62