Question

If 4,000,00 is invested at 5% interest compounded continuosly l, how much will the investment be worth in 25 years?

Answer 1

Answer:

$13,961.37

Step-by-step explanation:

Periodic compounding: P(1 + r/n)^Yn for n equal to

Incidentally, if you know calculus then the continuous compounding formula has a natural interpretation. First let's replace the clunky "FV" notation, and write f(t) for the balance at time t (with t measured in years). So  f(t)   =   Pe^tr

Taking the derivative

d/ dt f(t)   =  d/dt (Petr)   =   rPetr   =  r f(t)

In words, this is saying that

"at any instant the balance is changing at a rate that equals r times the current balance"

which of course is the definition of continuous compounding.