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